Iraq has become the newest front in the struggle for primacy between Saudi Arabia and Iran, with Riyadh mounting a determined bid to lure Baghdad out of Tehran’s orbit.But given the sheer magnitude of Iran’s influence in Iraq, this promises to be an arduous, if not impossible task.Saudi King Salman on Sunday hosted Iraqi Prime Minister Haidar Abadi for the first meeting of a joint coordinating council whose launch underscores the restart of ties after years of tension. Secretary of State Rex Tillerson participated in the meeting, with the US viewing Saudi-Iraqi rapprochement as a key means of isolating Iran. Tillerson hailed the opening of the Arar border crossing between Iraq and Saudi Arabia and the resumption of direct flights between them.On Saturday, Saudi Energy Minister Khalid al-Falih made a high profile visit to Baghdad, urging stronger economic relations to boost oil prices.Riyadh, which is combating Iranian influence in Yemen and Syria and sees an Iranian hand in outbreaks of unrest in neighboring Bahrain, has a clear interest in courting Iraq. “The Saudis want to woo the Iraqi government outside the orbit of Iran and drive a wedge between Iraq and Iran or at least enable the Iraqi government not to rely so heavily on Iranian support and reinforcement,” said Gabriel Ben-Dor, a Middle East specialist at the University of Haifa.The Saudis severed relations with Iraq in 1990, after Saddam Hussein’s invasion of Kuwait, and in more recent years relations were cool in light of Iran’s influence on Iraq’s Shi’a government. Iraq has a Shi’a majority and the religious bond gives Iran a natural advantage over Sunni Wahabi Saudi Arabia there, although a leading Shi’a cleric, Moqtada Sadr, has been criticizing Iran and recently visited Saudi Arabia.Abadi has aspirations for a more independent foreign policy than his predecessor Nouri al-Maliki, who was pro-Iran. “He is trying to gain freedom of action and increase Iraq’s independence by exploring a more robust relationship with the Saudis,” said Brandon Friedman, a scholar at Tel Aviv University’s Dayan Center for Middle Eastern and African Studies. “There are still a group of Iraqis who believe an independent, strong Iraq, not subordinate to Iran, is possible.”The rapprochement also has domestic imperatives for Abadi, since it sends a calming message to Iraq’s large Sunni majority, which has suffered exclusion especially under Maliki.”What Abadi really wants is more diplomatic support – to break away from the isolation Iraq suffered because of it being in effect an Iranian proxy – and to be accepted in mainstream Arab public opinion and in the inter-Arab scene,” said Ben-Dor. “He would like to appear as someone who represents the national interest in a patriotic way and not just a Shi’ite ruler who carries out the commands of Iran automatically. [Rapprochement] is very important for his effort to put the house in order.”But despite the interests on both sides, Iranian opposition might thwart the relationship from taking firm hold. “One can’t overstate Iranian influence in Iraq,” Friedman said. “If Iran doesn’t want to see something happen in Iraq, the question is not what levers does it possess, but rather what levers doesn’t it possess?” “Iran has deeply penetrated almost every institution of government in Iraq,” Friedman said.The powerful interior minister, Kasim al-Araji, has deep ties to Iran dating back to the 1980s, and comes from the Iranian-sponsored Badr paramilitary force.Iran has influential allies in the Iraqi Parliament to pursue its agenda. “Right now, if Abadi tried to manufacture a break, the Iranians would bring him to heel,” said F. Gregory Gause, head of the International Affairs Department at the Bush School of Government and Public Service at Texas A&M University. “At a minimum, they have influence over enough people in his parliamentary majority to make life difficult for him governing and perhaps even to have a no-confidence motion.”Iran also exerts wide influence through the Shi’ite militias it backs that participated in the war against ISIS. In a clear sign he will proceed cautiously in forging the Saudi ties, Abadi flatly rebuffed a call by Tillerson to “send home” the militias, with the premier saying the Iranian-backed Popular Mobilization Force is “part of the Iraqi institutions.” According to Reuters, Abadi said: “Popular Mobilization fighters should be encouraged because they will be the hope of the country and the region.”In the view of Gause, it is possible to dilute Iranian influence in Iraq, but it will take time. “You have to have a time-frame of years, not weeks or months. If you are the Saudis, you provide some help, political and economic, to the Iraqi government and friendly Iraqi politicians. You support the Iraqi army versus Popular Mobilization units and you wait for issues in Iran to maybe lessen the willingness and ability of the Iranian government to take an active role in Iraq. Who knows when the next political crisis in Iran will come, when their energies are focused more inside and less to their position in the region? If you’re an Iraqi prime minister, you can take advantage of those kind of events to re-consolidate in a way that makes you less reliant on Iran.” Gause added: “The Iranians have been building their position in Iraq since 2003. The Saudis didn’t get that involved. There’s ground work to be laid. It’s not going to happen tomorrow. But if you are willing to take a longer time frame, it is possible to compete with Iranian influence in Iraq.”Friedman is more skeptical: “From my perspective, it may be too late,” he said.