The Iraqi government agreed late Tuesday to start negotiations with U.S. officials on whether to authorize the U.S. military to remain in Iraq on a mission training Iraq's security forces after 2011.

The announcement came the same day that Adm. Michael G. Mullen, chairman of the Joint Chiefs of Staff, visited the country and warned that Washington needed a clear signal from Iraq about whether it would ask the American military stay on.

Senior Pentagon officials have been imploring Iraq's government for months to make a decision on a continued U.S. military presence, and last month, on a visit to Baghdad, Defense Secretary Leon E. Panetta expressed that frustration by saying, "Damn it, make a decision," referring to the Iraqis.

As a candidate, President Obama promised to end the Iraq war, so the White House has been reluctant to call openly for U.S. troops to remain.

But the top Pentagon officials generally favor keeping a small U.S. force here, fearing that a complete withdrawal will cause sectarian and ethnic fighting to intensify. Pentagon officials privately acknowledge that having troops in Iraq could also serve to deter neighboring Iran from asserting itself in the region. Mullen warned Tuesday of Iran's ambitions to meddle in Iraq.

Under Pentagon pressure, the White House this summer agreed privately to permit a maximum force of about 10,000 troops to assist with intelligence gathering and to mentor Iraqi troops.

The U.S. troop presence is one of the most contentious issues for Iraqis.

At Tuesday's five-hour closed-door meeting in Baghdad, senior Iraqi leaders gave the go-ahead for talks with the U.S. and also paved the way for Iraq's feuding political factions to end their disputes.

Foreign Minister Hoshyar Zebari said after the meeting that the negotiators would include Prime Minister Nouri Maliki, government advisors, the foreign minister and security ministers when they are finally named.

He said details still needed to be worked out, and he described the session as contentious. Still, the meeting ended with a consensus that talks had to begin.

One of the biggest obstacles before the meeting was the political stalemate that had pitted Maliki's coalition against his secular Shiite rival, Iyad Allawi.

The dispute between the men, who finished in a near-tie in 2010 national elections, has resulted in Iraq still not naming its defense or interior ministers. Maliki has been running both ministries.

At the meeting, the two sides agreed that Allawi's Iraqiya bloc would submit at least three names for defense minister and Maliki's coalition would do the same for interior minister. They would then attempt to choose the ministers at a meeting in two weeks.

Similarly, they agreed that legislation for a new national strategic policy council, to be headed by Allawi, would be submitted to parliament for approval, months after the body was supposed to have been formed. However, the sides still have to agree on how Allawi would be sworn in as head of the body. Allawi has said he should be approved by parliament; Maliki insists it should happen inside the new council. The dispute has held up the completion of a government since December.

An Iraqiya official expressed optimism that Maliki would move quickly on a security agreement with the Americans because Iraqis know that the U.S. military drawdown will accelerate in September, with all American troops scheduled to leave at the end of the year.

The official predicted that the country's political leaders, with the exception of Shiite cleric Muqtada Sadr, would now be likely to support an agreement in parliament granting U.S. forces immunity from legal prosecution in Iraq if they are serving in a training mission rather than a combat one.

Mullen wants the Iraqis to make a decision soon.

"Time is quickly running out for us to be able to consider any other course" but to leave, Mullen told reporters at the Camp Victory base, headquarters of the U.S. military in Iraq.

He also warned that the U.S. government would not accept any deal granting U.S. troops immunity from Iraqi prosecution if it did not pass parliament. Maliki and Zebari had previously argued that any deal for security trainers could be reached between the ministry involved and the U.S. government, but American officials said that would not provide enough protection.

About 46,000 U.S. forces remain in Iraq.

Zebari cautioned that the outcome of any talks on a continuing U.S. military presence was unpredictable.

"There aren't any foregone conclusions," he said.