Hopefully someone can chime in with a more complete answer on this, but I believe answer is yes. During the Greco-Turkish war Greece got a bit uppity because they thought that they had the full support of the Allies despite being a relatively weak nation. They attempted to steal a bunch of territory from the fledgling state of Turkey. Turkey pushed them back and managed to retake all of the land claimed by Greece in their initial conquest. At the end of that war there was a massive population exchange in which all of the "Turks" were evicted from Greece and sent to Turkey and all of the "Greeks" were evicted from Turkey and sent to Greece. To me this exchange of populations suggests that both Turkey and Greece were interested in expanding their territories further but decided it was easier to just accept things as they were and switch around the controversial portions of their populations.
Despite the population exchange, the Turks and the Greeks still lived in close quarters in Cyprus because Cyprus was, and still is, an independent nation; except for Northern Cyprus which was claimed by the Turks following the 1974 coup in Cyprus. The Turks claimed that they took over the territory in an effort to protect the Turks that were living on the island, but to this day they have never given back the land they took over which implies that they were interested in more than protecting the Turkish Cypriots.
It is also important to remember that the original Turks were mainly Ottomans who were used to living in a massive empire. Many of those that went on to create and fight for Turkey had fought throughout the Middle East in WWI trying to defend the Ottoman Empire. The diaries of many ex-Ottoman officers have shown that they were loyal to the empire until the very end. So I don't think it is unlikely that during the establishment of Turkey there would have been feelings of resentment towards the Allies and a desire to procure more land and reestablish the mighty Ottoman Empire.
For a succinct overview of the Turkish history mentioned here I would check out chapters 10 and 14 of Cleveland and Bunton's A History of the Modern Middle East. For more insights into how Ottoman military officers felt about the empire during and after WWI I recommend Leila Parson's The Commander.
It depends how you see it. In the period 1912-1923, there was obviously a desire to take back more land by Turks. Indeed, they not only desired it, they actually took it. That's what gave Turkey its current borders. However, by 1923, most of this desire for more land had subsided as the 1923 borders included most major Turkic populations that could be plausibly included. However, in three areas (Mosul, Hatay, and Cyprus) the Turkish Republic did try to incorporate borderlands Turkish populations into Turkey proper. I should also add that while these border adjustments were common up until WWII (indeed, WWII was predicated on them), they became very rare globally in the post-1946 world order. I discuss that more in this older answer. This essay has two parts spread over three posts.
Part I: Turkish Nationalism as Already Successful
Specially on Turks, this map gives what's probably a fairly accurate view of the ethnic distribution of ethnic groups in Anatolia and the Balkans in about 1911, that is before the Balkan Wars, World War I, the Murder and Expulsion of Ottoman Christians (i.e. the Armenian Genocide, the Greek Genocide, the Assyrian Genocide), the Turkish War of Independence, the voluntary population exchange between Turkey and Greece, etc. which changed the demographics of these areas and made them generally more homogenous. Now, the map has some inaccuracies: we know that the area around Antioch (modern Anatakya) was mixed Arab and Turkish, though this map shows it exclusively Arab, and that the Black Sea Coast was likewise mixed Greek, Turkish, and Laz, whereas this map shows it as exclusively Greek. Likewise, the Turkish bloc in Bulgaria was more mixed and there's another Turkish bloc in Southern Bulgaria that's less mixed. The Albanians in Greece are a mess, I think they're trying to show the Arromanian (Romanian) population in Greece, but grossly overestimating while seemingly omitting entirely the Albanians in Epirus who were expelled after WWII. Take this as a very general approximation, the best available, but a map, not a perfect representation of the situation. "Map is not territory".
Notice, though, that the modern state of Turkey does an excellent job of including most major contiguous blocs of ethnic Turks on the map, and even includes several regions that the map indicates as Greek, Kurdish, Armenian, and Arab. The only two notable blocs on the map not included in the 1923 border of Turkey are those in modern Bulgaria and those in historical Macedonia (both in northern Greece and the Former Soviet Republic of Macedonia).
This was by no means promised: since Bulgaria became autonomous in 1878, and arguably since Greece had achieved its independence in 1832, Ottoman-Turkish control of the Balkans looked increasingly unsteady. Turkish nationalism was pretty directly a response to this, and Erik Jan Zürcher has noted that the Turkish nationalists of the early 20th century were all "children of the borderlands", that is, not Turks from Anatolia, but Turks from border regions where they were possibly minorities, especially regions of the Balkans, Thrace, and the Aegean Coast which were particularly at risk of ending up in Christian-majority countries, though some like Ziya Gökalp were from borderlands like Diyarbakir, which was mixed Turkish and Kurdish.
From Balkan Wars to World War to Turkish War (of Independence)
I won't go into many details of the more or less continuous set of wars in the Balkans and Anatolia between the First Balkan War in 1912 and the Treaty of Lausanne in 1923, but suffice to say that the Turks had little hope or ambition of reclaiming the city of Salonica (which, I want to point, was plurality Spanish-speaking Jew, of all things, at the start of this period, with roughly 60 thousand Jews, 45 thousand Turks, and 40 thousand Greeks, as well as five thousand Bulgarians). Since the start of the First Balkan War, Greece and Bulgarian bought fought over the city, though by the end of the Second Balkan War, the city was firmly under Greek control. The Ottomans, and later the Turks, were much more concerned maintaining the city of Edirne (sometimes called Adrianople in older documents), the largest city in Thrace and the third Ottoman Capital (after Iznik/Nicaea, Bursa/Prusa, and before Istanbul/Constantinople) which was important for both strategical and nationalistic reasons. Securing Edirne was the major goal for Turkish and Ottoman forces in the region following the loss of Salonica in the First Balkan War. Edirne was briefly conquered by Bulgaria in the First Balkan Wars, and getting it back in the Second Balkan War was one of the few Ottoman/Turkish successes in this period. It was lost formally lost in the post-WWI Treaty of Sevres in 1920, but regained in the post-Turkish War of Independence Treaty of Lausanne in 1923. Indeed, the potential loss of Edirne was one of the pretexts for the 1913 coup by the Turkish nationalist Committee of Union and Progress (CUP). So Edirne, not Salonica, was after 1912 the point in the region that the Turkish nationalists desired to hold/take back.
In other areas you see similar things: Izmir/Smyrna was briefly conquered by the Greeks, but taken back at huge cost to the city. This is still remembered in Greece as the Asia Minor disaster. This map does a good job at showing the gradual expansion of the Greek state. One of the original ambitions of the Greek nationalist "Megali Idea" was Constantinople/Istanbul (notice the post-1920 "demilitarized zone" around the straights , a goal that was decisively stopped in 1923 with military defeat. For more on the Megali Idea, see this post.
Kars had been under Russian Imperial control 1878, but was by 1921 back under the control of Turkey, with the signing of the Treat of Wars, in which Turkey got Kars, Iğdır, and Ardahan in exchange for giving up Adjara/Batumi in modern day Georgia. This is a remarkably successful change of circumstance, since in 1916 Russian forces had managed to conquer Trabzon/Trebizond, Erzincan/Erzingian, and Erzurum, that is, all of Northeastern Anatolian and held it until they voluntarily withdrew due to the changing political situation at home due to the Russian Revolution. Once the Russians left the Caucasus, Ottoman forces were able to conquer all the way to Baku by late 1918, though that territory proved impossible to hold. Among those around Mustafa Kemal, rather than Enver Pasha who led the charge, there seemed little desire to try again to control Baku or other more distant Turkic lands that had little connections to the Ottoman Empire. The Soviets tried to reopen the issue of land in Eastern Anatolia in 1940's and 1950's, but unsuccessfully.
(continued below)
As for the relations between Greece and Turkey, while Kemal was alive, the relations were simply exemplary. There are several reasons for this co-operation. Republican Turkey was a natural partner for Greece because both countries perceived irredentist and expansionist Bulgaria and Italy as possible threats. In 1928, Greece and Turkey officially declared that they had no hidden expansionist agendas concerning each other. Greek Prime Minister Venizelos visited Turkey in 1930, to sign several treaties which would put an end to the problems derived from the aforementioned population exchange, promote closer cooperation between the nations and limit the sea forces of the two countries. Turkish PM Inonu returned the visit in 1931. Common fears concerning Mussolini's Mare Nostrum policy brought the countries even closer in 1930s. The good relations reached to their zenith with the Entente Cordiale signed in 1933 which guaranteed joint defence of the shared borders against a possible Bulgarian attack. A year later, Turkey and Greece formed the Balkan Pact with Romania and Yugoslavia. The Greek-Turkish relations reached such heights, that after 1935, the Greek and Turkish consulates, in countries which either one of them did not exist, started to pursue the benefits of the other country. For example, in Tehran, Turkish ambassador Enis Akaygen officially represented Greece and acted as a de facto Greek ambassador. As a further sign of the alliance between the two countries, Venizelos nominated Kemal for a Nobel Peace Prize in 1934. I think these examples above clearly depicts that Republican Turkey did not have any desire to take land from Greece.
As for the ideological background of this policy, we have to keep in mind that the Republican foreign policy was mostly the brainchild of Kemal. Therefore we have to understand his mindset, as well. He was a paradoxical figure; although being a staunch nationalist, he was an universalist as well who believed in the universality of humanity and the common values of the Enlightenment. He claimed that the entire humanity was a single, common body and each nation was a different, yet equal organ of that common body. Expansionism, was therefore against his system of values. More interestingly, he perceived expansionism as a relic of the past, a disease of the Ottomans. In one speech, he claimed that although once "Turkish land was much greater", after the establishment of the Republic, Turks were more content with the new borders of the country and criticized the previous Ottoman policy of expansion. He blamed the Ottoman sultans for forgetting the needs of the people of Anatolia and for pursuing unrealistic dreams of world domination instead of developing the agriculture and industry of their homeland.
Republican ideology was based on the concept of modernization and to achieve this feat Kemal envisaged " a total civilizational leap", from the Eastern one to the Western one. Therefore, expansionism, which he associated with Ottoman and "Eastern" mentality had to be replaced by a more peaceful, and flexible foreign policy. Furthermore, invading new lands meant adding new people to the nation, it meant a multi-national country which he strongly refused. He believed that each nation should be a monolith, undivided by differences based on class, gender, religion, or ethnic identity. He pursued a policy of Turkification in Turkey, and tried to assimilate the different linguistic communities, following the French, and Italian models. According to Davison, he ridiculed multi-national states, and due to his policies the "Turks never seriously thought of trying to reconstruct the old Ottoman Empire and to incorporate again ... the lost territories." Therefore it is safe to assume both for practical and ideological reasons Turkey did not pursue expansionist policies. Furthermore, in the interwar era, in the international sphere, Republican Turkey always remained in the status quo camp; they criticized the Italian take-over of Ethiopia, and the illegal de-militarisation of the Rhineland by Germany while supporting the Republican forces in the Spanish Civil War.
In summary, instead of taking more lands, they targeted a more cohesive society based on assimilation of various different identities in a new, modern, secular Turkishness, and they tried to integrate this new, modern nation-state they created to the "Western civilization".
The answer is a definite no; Turkish Republic, right from the start only interested in a smaller, more manageable Turkey, with a more homogeneous (Muslim) population. The Turkish foreign policy in the early Republican era was non-expansionist and non-irredentist. They enjoyed very good relations with their traditional enemies (such as Russia and Iran) and with the countries which were once part of the Ottoman Empire (such as Greece). Throughout the inter-war era Turkey remained as an active member of the status quo camp and therefore it was defined "as a force of stability" in the world by the prominent historian Eric Hobsbawm. This policy was a product of both practical and ideological concerns. In this response, I am going to explain mostly the ideological background of these policies, but before that I am going to briefly discuss the historical background. Since the question specifically mentions Ataturk, I am going limit myself with the early Republican era, which lasted roughly from 1920 to 1945. Since my response will most probably be above the character limit, I am going to divide it in two parts.
Historically, this peaceful foreign policy started even before the official establishment of the Republic in 1923. During the Turkish nationalist struggle (which is also known as the Turkish War of Independence) which lasted from 1919 to 1923, the nationalists which were led by Kemal, wanted to present their struggle as a rightful and legal one. They based their claims of a free, independent Anatolia on the twelfth point of the Wilson Principles which guaranteed the sovereignty "of the Turkish portion" of the Ottoman Empire. Therefore they repeatedly announced that their only aim was to defend the territory which the Ottoman government controlled during the Armistice of 1919. They had no claim in Western Thrace (modern day Greece) or in the Arabic parts of the Empire. For instance, at that time a separate Turkish nationalist movement already existed in Thrace but the nationalist government refused to help them. Similarly, in 1920 Kemal stated that the nationalist government represented solely the Muslims of Anatolia, and therefore they did not have the authority or the will to make any claims in the name of the Arabic citizens of the Ottoman Empire. Furthermore, he refused the please of the fledgling pan-Turkist movement which wanted an expanded Turkish Republic including both Northern (modern day Republic of Azerbaijan) and Southern Azerbaijan (the Turkish speaking region of Iran). Although the nationalist army controlled most of these regions at that time, Kemal made a deal with the Soviets and gave his word to Lenin for the installment of a Soviet government in Azerbaijan in exchange of diplomatic recognition and financial aid. Therefore, even before the establishment of the Republic, the new ruling elite made it clear with their actions that they will only pursue defensive policies within the limitations of the international law.
After repulsing the invading Greek forces, the army of the Turkish Assembly stopped its advance and the government continued to pursue diplomatic means to make a revised treaty with the Allies which they managed to do in 1923. When they signed the Lausanne Treaty with the Allies, some regions which was accepted as integral parts of Turkey by the last Ottoman Assembly in a decision called "Misak-i Milli" (The National Pact), have remained outside of the new map of the Turkish Republic. These regions did not include any parts of Greece or Cyprus. On the other hand, regions such as Mosul (in modern day Iraq - under British control in 1920s), and Alexandretta (was in Syrian Mandate which was under French control in 1920s) were considered as a part of the Pact, because the last Ottoman Parliament believed that the majority of the population of these regions were made up by Turks and Kurds, and therefore they should not be under the control of the newly-founded British and French quasi-colonies in the Arabic heartlands. For the Arabic populated parts of the Ottoman Empire, they were no such demands. The new Turkish Assembly, and its leaders believed that the co-existence between Arabs and Turks which lasted for a millennium came to an end after the war. Therefore they did not even contemplate to demand the ex-territories of the Empire (such as Tunis, Algeria, Libya, Egypt, Syria, Iraq, etc.). For the two regions mentioned above, the Republican Turkish government only followed diplomatic means in 1920s and 1930s and these issues were brought to the attention of the League of Nations (the predecessor of the UN). The League decided that Alexandratta should belong to Turkey, and Mosul should remain as a part of the British mandate. To continuing to control Mosul and to compensate Turkey's lost, Britain paid a healthy sum to the Republican government.
The Turkish-Greek relations in the inter-war era is a perfect example of the peaceful Turkish foreign policy. It is impossible to interpret the population exchange as an expansionist idea. This policy was mostly related to the nation building project pursued by these two nations. At that time, both countries were trying to homogenize their population to establish nation states. In the post-WWI world, nation states were seen as the epitome of modernity and most politicians (including Wilson) assumed that the nation-state model would bring an end to the conflicts between the nations. Therefore it felt very natural for the Greek and Turkish governments to clearly separate Greek and Turkish people from each other. This exchange had nothing to with expansion, in fact it is the acceptance of the contraction of territories. Secondly, it was also the acceptance that the imperial and cosmopolitan models were the reasons of the sufferings of these people. The leaders of Greece and Turkey, as well as the international authorities thought that with a population exchange the atrocities between Turks and Greeks would stop for good. Therefore in 1923 nearly 1.2 million (this number includes the Greeks who escaped from Anatolia in 1922 fearing from the Turkish nationalist backlash after several atrocities performed by the invading Greek forces between 1920 and 1923) "Greeks" (in reality Greek Orthodox people as a user mentioned above, for instance Orthodox people from Turkish ethnicity were also sent to Greece) migrated to Greece from Anatolia while most of the Muslims living in Greece (600.000 people in total, including Muslim Greeks and Bulgarians, as well) came to Turkey. The population exchange plan was designed to protect both of these minorities and was championed by a Norwegian diplomat who received the Nobel Peace Prize that year for his efforts on this matter. After the war there were similar population movements all around Europe as well, all states were trying to establish more "homogeneous societies". Although the results were extremely tragic for these people (for instance some "Greeks" forced to go to Greece did not speak Greek at all, similarly some of the "Turks" who were forced to settle in Anatolia did not speak Turkish), the population exchange was in perfect harmony with the zeitgeist of that era.
Yes there was a pressure to take it back since the greek army was in complete ruin. But Mustafa Kemal was a realist, he didn't let his emotions get the better of him. Instead, he used the resources needed for such an undertaking on social development, and betterment of the turkish nation as a whole.
