IRBIL, Iraq - Iraqi Shiite Muslim militias, angry that the government of Prime Minister Haider al-Abadi has asked for American help in ejecting Islamic State fighters from the central Iraqi city of Tikrit, began Thursday withdrawing their forces from the battle, the first major break between the Iranian-trained militias and Iraq's military establishment since the Islamic State advance last year.

Whether the militias, which have formed the backbone of the Iraqi response to the Islamic State since Iraq's army collapsed last summer, would continue to participate in the fighting was undecided. Militia members told McClatchy that their commanders were meeting to decide the issue.

But the withdrawal of the militias with their Iranian advisers would be a victory of sorts for U.S. officials, who have warned repeatedly that the Iraqi government's dependency on sectarian organizations fed support for the Islamic State among Iraq's disaffected Sunni Muslim population.

One Iraqi security official said three major Shiite groups - the League of Righteousness, the Kateb Hezbollah, and the Badr Organization - already had withdrawn their forces. The official, who asked not to be identified discussing sensitive military matters, said he had been told that the militia commanders were meeting late Thursday to decide whether to remain or return to Baghdad, where many had mustered last summer in response to the Islamic State advance.

"Militia leaders have assured us that all militias will be represented" at the meeting, the official said. "Participants will decide either to participate or withdraw."

One militia officer, who also spoke anonymously, said that many militia remained arrayed outside Tikrit with their Iranian advisers. He said both the militias and their advisers opposed American participation in the offensive. "They object as much as we do to the participation of the Americans in this noble operation to liberate Iraqi land from Daash," he said, using an Arabic term for the Islamic State.

The withdrawal of the militias from the battle for Tikrit would be a dramatic reversal of Iraqi tactics to stem the Islamic State's advance.

In the first months after the Islamic State captured Mosul, Iraq's second-largest city, last June, then raced across northern and central Iraq, Shiite militias were credited with preventing the capture of some crucial cities, including Samarra.