WASHINGTON — Iran’s growing influence in Iraq is setting off alarm bells, and nowhere is the problem starker than in the high-stakes battle for Tikrit. It marks a crucial fight in the bigger war to expel the Islamic State group from Iraq, and yet Iran and the Shiite militias it empowers – not the U.S. – are leading the charge.

This is both a political and military dilemma for the Obama administration, which is under heavy criticism for negotiating with Iran over limits on its nuclear program. Iran, meanwhile, is asserting itself in a divided Iraq like never before.

The battle for Tikrit raises the question: Who is really running this war? Iraq? The U.S.? Iran?

Defense Secretary Ash Carter, under questioning from Sen. John McCain this week, acknowledged his concern when McCain asked if it alarms him that Iran “has basically taken over the fight.”

“It does. It does,” Carter replied, adding, “We’re watching it very closely.”

Watching, but not participating.

The Iraqis did not ask the U.S. led-coalition to coordinate or provide airstrikes in support of the Iraqi ground forces in Tikrit, even though it was largely U.S. air power that halted Islamic State advances after its fighters swept across northern Iraq last summer and captured key cities, including Tikrit and Mosul, as the Iraqi army quickly folded.

Instead, Joint Chiefs Chairman Gen. Martin Dempsey told McCain’s committee, about two-thirds of the Iraqi forces fighting for Tikrit are Shiite militias supported by Iran. The rest are regular Iraqi soldiers.

The issue is the two major powers – the U.S. and Iran – might be running parallel campaigns with different goals. Both want the Islamic State group out of Iraq, but the U.S. hopes for an inclusive Iraqi government that includes Sunnis, Shiites and Kurds. Iran, the major Shiite power in the region, would prefer a largely Shiite Iraq.

The Iranian involvement has also raised concerns among the U.S. coalition fighting the Islamic State group in Iraq and Syria.

“What is happening in Tikrit is exactly what we are worried about. Iran is taking over the country,” Saudi Foreign Minister Prince Saud al-Faisal said Thursday in Riyadh with Secretary of State John Kerry.

Kerry, however, said he was glad to see the Iraqi government taking the lead, even if it meant Iranian involvement.

“This was put together by the Iraqis, formulated by the Iraqis, executed by the Iraqis, and that’s the best thing all of us could, frankly, ask for,” Kerry said. “So we take it the way it is and we’ll hope for the best results and move from there.”

Tikrit is ripe with irony. It is the birthplace of Saddam Hussein, who led Iraq into a devastating 1980-88 war with Iran. Now Baghdad has embraced Iranian military leadership in the fight for Tikrit, to the exclusion of the Americans, who invaded Iraq 12 years ago to topple Saddam and lost thousands of lives trying to ensure a stable, multi-sectarian and independent Iraq.

Stephen Biddle, a professor of international affairs at George Washington University and a consultant to U.S. commanders, said the Iraqis see the Iranians as a convenient alternative to the Americans as Washington pushes Iraq to be more accepting of Sunni political interests.

“So if we push them too hard they can just go to the Iranians,” Biddle said. “The Tikrit offensive is a terrific example of that in practice.”

Dempsey called the Iranian involvement in Tikrit “the most overt” Iranian military support thus far in Iraq’s campaign against IS, but he held out hope that it could work out.

“Frankly, it will only be a problem if it results in sectarianism,” Dempsey said, referring to the fact that the Shiite militias could inflame sectarian tensions in Sunni-dominated Tikrit.