The United States persuaded Iraq to sideline Iranian-backed Shiite militias as a condition of American airstrikes in the strategic city of Tikrit, a senior U.S. general said Thursday.

The move limits Iran’s influence in Iraq, at least temporarily, and could re-invigorate a ground offensive that U.S. officials said had become stalled under Iranian leadership.

Army Gen. Lloyd Austin, head of U.S. Central Command, told a Senate hearing that he had insisted that Iranian-backed militias pull back before the U.S. began flying intelligence-gathering flights over the weekend and dropping bombs Wednesday in support of a reconfigured Iraqi force of soldiers and federal police.

Spokesmen for a number of the Shiite militias countered that they had chosen to withdraw from the battle for Tikrit in protest of the United States entering the fray.

Either way, the conditions set for U.S. airstrikes were an important turn of events, given U.S. concerns that Shiite-majority Iran’s role in Tikrit had unsettled its anti-Islamic State group coalition of Sunni Arab states like Saudi Arabia, that see Iran as an adversary and worry about spread of Iran’s influence.

Tikrit is a predominantly Sunni city and the hometown of former Iraqi leader Saddam Hussein.

The predominant role of Iranian-backed militias in the early stages of the battle to retake Tikrit from Islamic State fighters also raised concerns that the offensive could deepen Iraq’s sectarian divide and drive Sunnis to the militants.

While the U.S. has bombed Islamic State targets in much of northern and western Iraq nearly every day since August, it had until now been a bystander in Tikrit, saying Baghdad had not requested help. The Iraqis said they intended to liberate the city on their own, while acknowledging they were getting help from Iranian military advisers and arms.

Offering an explanation for “why it failed,” Austin said the attempt to quickly recapture Tikrit with Shiite militias lacked precision firepower, proper command from the Iraqi government and a coherent plan for maneuvering ground forces against a dug-in enemy.

Iraq also lacks a sophisticated air force. The introduction of American air power is intended to open the door for Iraqi ground forces to enter the city in coming days or weeks. Strikes continued Thursday.

Referring to the Shiite militias armed, trained and advised by Iran, Austin said, “These forces obviously were not being controlled by the government of Iraq.” That is a bold statement, given the Iraqi government’s assertion that it had effectively and deliberately balanced its partnerships with the U.S. and Iran, which is a neighbor.

Austin cited not only what he called the militia’s ineffective leadership in the Tikrit offensive but also his painful recollection of how American troops fighting under his command during the Iraq war had been “brutalized” by Shiite militias.

“I will not, and I hope we never, coordinate or cooperate with Shiite militias,” he told the Senate Armed Services Committee.