Prior to World War One, the Ottoman Empire was the sick man of Europe. It lost a war to Italy in 1911, the First Balkan War in 1912, and joined forces with Greece, Serbia and Romania, to cut Bulgaria down to size in the Second Balkan War of 1913. The Ottoman Empire recovered what is still Turkey's European territory.
The Treaty of London, in 1915 saw Great Britain agree to Russian control of the Dardanelles and Constantinople. Greece would get the south western corner of Anatolia. Italy also had a small claim on a slice of the Ottoman Empire. After World War I, Greece was the only country that made a strong bid to take their claim. Attaturk was able to defeat the Greek army and entered Smyrna on September 9th 1922. This set off a major round of bi-lateral ethnic cleansing. Roughly 500,000 ethnic Turks and Greek Muslims had to move out of Greece and back to Turkey. 1,500,000 Greeks and Orthodox Christians were forced out of Turkey under the terms of the Treaty of Lausanne. It ended a bloody war that saw more than 400,000 Greek civilians killed and many Turkish villages burned by the Greek army.
The Italians were broke after World War One and sent only minor forces to Turkey from 1921 to 1923. The Royal navy and French navy were anchored off of Constantinople, but they did little or nothing to help the Greeks. The Soviet Union had defeated the White armies in the Russian civil war, but Lenin was still enforcing "War Communism" and was forcibly trying to socialize the peasants in the USSR. They resisted these efforts with groups of irregular partisans, known loosely as the Greens. The Russian civil war was still raging in 1921-1923 and the Soviet Union was in no shape to try and press their claims on the gateway to the Black Sea.
Source: "Ghost on horse back: the story of Mustafa Kemel Attaturk" by Ray Brock
"The treaty of Lausanne, 1923" by Dinah Shelton