BAGHDAD — The leaders of two rival political alliances battling to run Iraq’s new government took a step toward ending their power dispute Saturday, as the Sunni-backed coalition that won March elections now faces being sidelined in parliament.

The 90-minute meeting between Prime Minister Nouri al-Maliki and former Premier Ayad Allawi was their first since the March 7 vote, and was described by aides as more of an icebreaker than the start of serious negotiations.

The secular but Sunni-dominated Iraqiya coalition that Allawi heads risks losing a grasp on its narrow electoral triumph due to infighting and outmaneuvering by al-Maliki and his fellow Shiite rivals.

As the new legislature convenes Monday, that prospect is serving as a lesson in Iraq’s nascent democracy, where rules can bend. It also, more ominously, raises the possibility of a revitalized insurgency if Sunnis conclude that they have no place in government as U.S. troops pull out of Iraq.

“That’s why it’s important to have a unity government,” Army Gen. Ray Odierno, top U.S. commander in Iraq, told a Pentagon news conference last week. “We don’t want to see any group that feels it’s been disenfranchised and even contemplates moving back to an insurgency.”