Iraq’s military this week launched its most ambitious offensive yet to roll back the Islamic State in Iraq and the Levant (ISIL), moving to recapture the city of Tikrit in an operation seen as a dry run for its planned march on Mosul, Iraq’s second city and the most important holding in ISIL’s self-declared caliphate. The offensive is backed in the field by forces from the Iraqi government’s most important ally, Iran, leaving the United States in the awkward position of taking a backseat to its longtime antagonist.

The force, which by Thursday had encircled Tikrit, Saddam Hussein’s hometown, consists of an amalgam of Iraqi army regulars, Shia militias and, reportedly, a faction from Iran’s Islamic Revolutionary Guards Corps. Noticeably absent was the U.S., which will not provide air support for this campaign against ISIL, although it has across Syria and Iraq for months. The U.S., analysts said, wants to distance itself not only from Iran but also from the Tehran-backed Shia militias, which have a track record of engaging in sectarian violence against local Sunni civilians.

The Tikrit campaign lays bare the layered dilemmas facing the U.S. in Iraq. For months, Washington has sought to paint its war against ISIL as separate from, if parallel to, that of Iran and its Shia proxies — a line is growing harder to maintain. As Tikrit shows, the U.S. is uneasy about the leading role Iran has taken against ISIL, an effort that is spearheaded on many fronts, including in Tikrit, by hard-line Shia militias that many say are liable to exacerbate the alienation of Iraq’s Sunni minority. Sectarian resentments were part of what made ISIL's surge across Sunni lands in Iraq last June possible, with Sunnis in many areas allowing ISIL forces to move in unchallenged or even providing local conscripts. With Iraq’s fight against ISIL taking an increasingly sectarian cast, the U.S. is staying behind the scenes, limiting its role to airstrikes or military advisers.

But there is nothing covert about Iran’s role. This week photos were circulated online of top Revolutionary Guards commander Gen. Qasem Suleimani rallying troops in the city of Samarra, where the Tikrit campaign was formally launched. The presence of Suleimani — who is accused of directing a Shia offensive on U.S. forces during the eight-year U.S. occupation after the ouster of Saddam — was seen by some as an affront to the U.S. and as a “flag-planting moment” for Iran, said Phillip Smyth, an expert on Shia militias and a contributing researcher to the Washington Institute for Near East Policy.

“We’re seeing far more open, direct Iranian involvement in Iraq than even in Syria,” Smyth said. Taken with the recent Shia Houthi takeover in Yemen, “from a big-picture perspective, the Iranians are projecting themselves regionally, while the U.S. is looking quite impotent.”

The specter of Iranian expansionism was raised by Israeli Prime Minister Benjamin Netanyahu in his address to Congress on Tuesday, in which he warned against a nuclear deal with Iran. Several Saudi officials and hawkish members of Congress, including Republican Sens. John McCain of Arizona and Lindsey Graham of South Carolina, have echoed that view. In a statement Tuesday, McCain and Graham argued that President Barack Obama’s unwillingness to expand U.S. military involvement in Iraq could have lasting implications for the country’s influence in Baghdad and beyond. "Success in this mission will not be achieved by capitulating to Iran’s ambitions for regional hegemony," they said.

“We’ve come to the unfortunate conclusion where if the U.S. really and truly wants to preserve its power, it has to project itself,” Smyth added.

Still, Iran’s role in the region is not new, nor is it one-dimensional. Each of Iraq’s democratically elected governments since 2005, after the fall of Saddam, a Sunni, have had a close relationship to Tehran. But some have cast doubt on the extent of the relationship between Iran and the Houthis in Yemen, since Tehran has formally denied arming them.

For their part, Pentagon officials have downplayed any strategic dilemma. Joint Chiefs of Staff Chairman Gen. Martin Dempsey said this week that the participation of Tehran-backed Shia militias in the Tikrit offensive could actually be “a positive thing,” as long as sectarian violence did not erupt.

And it isn’t clear what alternatives are available to the U.S. Iraq’s military remains highly dependent on Iranian support, without which it proved unable to even slow the ISIL surge last year. Iranian-backed Shia militias such as the Badr Organization have stepped in to hold the line, prompting some to warn of the Hezbollization of Iraq — referring to the powerful Iranian-allied Shia militia that functions as a state within a state in Lebanon, more powerful even than the national army. But with scant options among anti-ISIL Sunni factions and the U.S. public cool on being drawn into another ground war, “there’s really no other option,” said Matthew Henman, the head of IHS Jane's Terrorism and Insurgency Center.

A more immediate concern is that Shia militias will exact brutal revenge on Sunni civilians in Tikrit, given their history of bloody reprisal against Sunnis, whom they have collectively blamed for the rise of Al-Qaeda and now ISIL. In January, Iraq’s Prime Minister Haider al-Abadi ordered an investigation into allegations that Shia militias slaughtered more than 70 people in the town of Barwana, in Diyala province, after ISIL was driven out. Those reports, while unconfirmed, recall the days of Shia death squads during the civil strife of 2006 and 2007 — a worrying precedent for the Sunnis of Tikrit and Mosul, should the Iraqi offensive meet success.

Of course, a sectarian dynamic in which Sunnis turn to ISIL for protection from Shia attacks is exactly what ISIL has tried to provoke. The group “presents itself as the only credible force that can protect Sunnis,” Henman said. “If Shias seem to be enacting sectarian retribution, there is no chance Sunnis, many of whom are on the fence, will welcome in government forces in the future.” For that reason, analysts say, Baghdad and perhaps even Tehran have an interest in limiting sectarian violence that would further complicate their cause.

As for the existential fears of Iran’s regional influence, which has indisputably blossomed since the U.S. toppled Tehran’s main regional adversary, Saddam, Washington appears to have little recourse. “Concern has been expressed that the U.S. risks losing Iraq to Iran in the fight against [ISIL],” said Aymenn Jawad al-Tamimi, an analyst with the Middle East Forum, writing in The Daily Beast. “But it is probably more accurate to say the U.S. has already lost Iraq to Iran.”