Iraq never really had a formal alliance with the Soviet Union, there were various friendship treaties and pledges of military assistance such as 1972 Treaty of Friendship and Cooperation, but little in the way of a substantive relationship. The Iraqi Communist Party (ICP) supporting the warming of the Iraqi-Soviet relationship and participated in the National Progressive Front, an umbrella organization encompassing the Ba'ath, ICP, and Krudish Revolutionary Party. The ICP tended to act as a voice arguing for more closer alliance with the Soviets and a more strident line against imperialism.

Therein lies a goodly part of the reason why the ICP was purged from the National Front as the Ba'ath party solidified its power. The ICP combined a number of factors that made it dangerous to Ba'ath leaders like al-Bakr and Hussein. In a 1971 interview, the secretary-general of the Iraqi Ba'ath Regional Command, Abd al-Khaliq al-Samarra'i explained that there were two camps within the Ba'ath about the ICP:

Most of us were genuinely interested in an accommodation with the Communist Party. However, there were two camps in our leadership whose reasons for this cooperation were different. One group wanted to cooperate with them [ICP] to utilize their political and practical experience, their intellectual sophistication, and especially their theoretical grounding in social and international issues. Others, including Saddam Hussein and al-Bakr, felt we could not succeed as long as the communists were not under control, if not subdued, and within that group there were two factions: one, mainly conservative, the majority of whom were from the army and wanted the communists to be destroyed, and the others who wanted [the communists] to be neutralized and become an appendage to us.

One of the problems of sustaining a National Front with the ICP, and one al-Samarra'i pointed out in his interview, was that the ICP was one of the longest-established revolutionary parties in Iraq and had enjoyed a privileged relationship with the USSR that other parties, like the Ba'ath lacked. While al-Bakr sought to strong arm the ICP by neutralizing it via cultivating strong ties with the USSR, the faction around Hussein cut the Gordian knot and began a formal Ba'athist suppression of the ICP between 1977/78. The ICP responded accordingly with pamphlets more critical of Ba'athist policies and its dalliances with the West at the expense of the forces of revolutionary liberation.

The Soviet Union watched these developments nervously, but there was little it could do to stop them. When the Ba'ath launched a purging of the Iraqi military of ICP and communist sympathizers in 1977, Brezhnev appealed for clemency, but Ba'ath organs derided these appeals as Soviet interference into Iraqi domestic politics. The result was a Soviet-Iraqi relations entered into a chilled period with the rise of Hussein.

The early 1980s saw the nadir of Soviet efforts to court the Middle East during the Cold War as their networks of strategic partnerships with various Arab states collapsed. The Soviets had hoped that their sponsorship of various nationalist movements like the Ba'ath would lead to a cooperative relationship with local communist parties. In the 1950s and 60s, both Arab nationalists and Arab communists in the Middle East shared some ideological commonalities. They both believed in a centrally-planned economy, were leery of the Western powers, and advocated a secular modern state. The problem was as the Arab nationalist movements evolved into platforms for regional strongmen, the independence of communist parties became a threat. Saddam's suppression ICP was similiar to contemporaneous actions against Syrian communists undertaken by Assad and earlier Nasserite precedents. Reports from the GDR's security services show that many in the Eastern bloc were alarmed by this repression but Moscow reasoned that an open break with Iraq would undo whatever influence it had with Saddam.

The Soviets did give some assistance to ICP forces in Kurdistan and provided a safe-haven for ICP leaders in the USSR. This assistance to the ICP was tenuous and low-key, but increased as when Saddam quickly and publicly condemned the Afghanistan invasion in 1979. However, Iraq at this time began diversifying its arms suppliers and economic assistance packages. The Iraqis began courting Brazil, the FRG, China and other powers outside the control of Moscow. Saddam therefore ensured that he would have alternatives if Moscow fully broke off relations and thus he put a further squeeze on the ICP.

The outbreak of war with Iran caught Moscow quite flat-footed as it had believed that Tudeh (the Iranian communist party) could capitalize on the chaos of the Iranian Revolution and emerge as the head of a new Iranian state. Although this was highly unlikely and KGB efforts in Iran bore little fruit, the Iraqi invasion spelled their death knell. The Soviets declared an embargo on Iraqi arms and refused to honor existing contracts. Iraq's military reverses in 1980/81 led Saddam to backpedal on his anti-Afghanistan rhetoric as he realized he needed Soviet arms to maintain his armies as his attempts to buy replacements on the world market depleted Iraqi monetary reserves. The Soviets in turn decided to begin resupplying the Iraqis in the Summer of 1981. Again, guiding principle of the Soviets mirrored the same rationalization of supporting the Ba'ath in the 1970s: they had invested too much in Iraq alreadyto just abandon it.

Soviet aid to Iraq during the conflict was never consistent and ebbed and flowed throughout the Iran-Iraq War.The Iraqis also continued their policy of diversifying their defense suppliers, which further lessened the Soviet's leverage. Saddam's continued military incompetence meant that the Iraqis started to demand for more advanced Soviet equipment, in exchange, the Soviets demanded to examine captured Iranian weapons. But beyond this functional relationship, the Soviets hoped that by providing Hussein with enough armed force, they could compel Iran to a cease-fire. Once that was achieved, Moscow believed it could rebuild its influence in the region by sponsoring reconciliation between Iraq and Syria. Such aspirations proved illusory given the general collapse of Soviet power in Eastern Europe in 1989 which meant the Soviets could ill-afford to continue any sponsorship of Iraq after the invasion of Kuwait.

In hindsight, the brief partnership between the Ba'ath and the ICP in the National Front was something of a marriage of convenience. By virtue of its historical pedigree, ideological background, and connections to the USSR, the ICP's instincts was to be an autonomous actor in Iraqi politics and carve out its own niche inside Iraq. Such a development was looked on with great skepticism in Ba'ath circles, especially within the party's security apparatus, many of whom saw the ICP as dominated by both non-Arabs and foreign ideas. The suppression of the ICP also coincided with a number of other internal purges of the Ba'ath's National Front partners and potential rivals of Hussein inside the Ba'ath, including al-Samarra'i. While this repression heightened tensions with Moscow, the geopolitical importance of Iraq to the Soviet's crumbling Middle East policy meant Hussein had a greater deal of latitude to crush the ICP than he would have otherwise possessed.

Sources

Andrew, Christopher, and Vasili Mitrokhin. The World was Going our Way: the KGB and the Battle for the Third World. Basic Books, 2005.

Brands, Hal. "Saddam Hussein, the United States, and the invasion of Iran: was there a green light?." Cold War History 12, no. 2 (2012): 319-343.

Ismael, Tareq Y. The Rise and Fall of the Communist Party of Iraq. Cambridge: New York, 2008

Murray, Williamson, and Kevin Woods. The Iran-Iraq War: A Military and Strategic History. Cambridge University Press, 2014.

Sassoon, Joseph. Saddam Hussein's Ba'th Party: Inside an Authoritarian Regime. Cambridge: Cambridge University Press, 2011.

_. "The East German Ministry for State Security and Iraq, 1968–1989." Journal of Cold War Studies 16, no. 1 (2014): 4-23.

Takeyh, Ray. "The Iran-Iraq War: A Reassessment." The Middle East Journal 64, no. 3 (2010): 365-383.

Saddam Hussein admired Josef Stalin. Not least because he shared several personality and ideological traits in common with him-including a disdain for "human" or ideological factors in foreign policy, much to the dissatisfaction of the ideologically bombastic late 70s Kremlin, high off their successful mid-70s ideological offensive in the Third World. Saddam's admiration for Stalin, however, did not extend to a serious trust of late Brezhnev era Moscow. It most certainly did not extend tolerating KGB agents meddling with serious matters in Baghdad or letting the Soviet Union have any serious control over Iraqi policy. Saddam also, from a personality standpoint, entirely lacked the ability of a Hafez al-Assad to take his ego down a notch and "play the client game" in doing diplomacy with superpowers and avoiding trouble, as would be made brutally apparent in the 90s.

The Kremlin didn't like it, but due to the twin pressures of the Afghan War (widely unpopular throughout the Muslim World-they couldn't be picky about friends at the time) and the Iranian Revolution, turned a blind eye toward Saddam's disposal of Iraqi Communists. It was generally agreed upon that Saddam was irritating but by far the least worst option compared to the specter of a Shi'a (and possibly eventually pan-Islamic, as was Khomeini's long term hope) theocracy spreading to Iraq, much like the Nixon Administration decided in 1969 that Sihanouk was a pain in the ass, but the only realistic alternative to a Communist ruled Indochina. Moscow did everything it could to avoid an open breach with Saddam. One thing both superpowers in the early 80s held in common was that he was by far the lesser evil to Khomeini at the time, before that stupid Iran-Contra nonsense(my own personal sentiments here are irrelevant to this forum)... The occasional Soviet journal complained about it, but no serious measures were taken against Baghdad.

Still, Kissinger's famous dictum on why both sides of the the Iran-Iraq War couldn't lose probably fell on sympathetic ears in Moscow at times.