(AP) — The top U.S. military officer said Tuesday that American troops must be given immunity from prosecution as part of any agreement to keep them in Iraq beyond the end of the year and that this protection must be approved by Iraq's parliament.

The comments by Joint Chiefs chairman Adm. Mike Mullen could make it more difficult for the troops to stay here.

Mullen and other U.S. officials have been pushing Iraq to decide whether they would want additional American forces to stay in the country past their Dec. 31 departure date, and the immunity issue has been one of the key sticking points.

"An agreement, which would include privileges and immunities for our American men and women in uniform will need to go through the COR," said Mullen, referring to the Council of Representatives as Iraq's parliament is known.

Washington has offered to let up to 10,000 U.S. troops stay and continue training Iraqi forces on tanks, fighter jets and other military equipment.

Mullen told reporters in Baghdad that Iraq's president and prime minister have promised to quickly consider the offer, and stressed that time is running out.

U.S. officials have said repeatedly that they need to know soon whether Iraq wants them to stay longer so they can figure out which of their forces must stay and which must go. Right now, about 46,000 American forces remain in country, and this fall their departure will begin ramping up.

"A significant part of this is just a physics problem. You get to a point in time where you just can't turn back and all the troops must leave. That's why it's so important to make the decision absolutely as soon as possible," he said.

But Iraqi lawmakers and government officials have been leery about taking a public stand on whether they want American forces to stay or go.

U.S. troops are still unpopular with many Iraqis who are tired of eight years of war. One of Prime Minister Nouri al-Maliki's top allies, anti-American cleric Muqtada al-Sadr, has made it his mission to drive American forces from the country, leaving the prime minister in a tough position.

Mullen met Monday night with al-Maliki and Iraqi President Jalal Talabani. He said they know a decision must come soon but acknowledged that they face "internal challenges, associated with reaching this decision."

"They're very aware of the urgency of the issue," said Mullen. "It was apparent to me in meeting with both the prime minister and the president that they're anxious to resolve and reconcile those differences. but that's really up to them."

Al-Maliki said in a statement on his website late Monday that he hoped Iraqi political blocs would be able to reach a consensus Tuesday night when they are expected to meet.

The Shiite prime minister stressed that regardless of the decision on U.S. troops that he wanted Washington and Baghdad to continue cooperation, especially in the area of air defense.

Iraq is unable to provide for its own air sovereignty. Over the weekend al-Maliki announced that Iraq would purchase 36 F-16 fighter planes from the U.S., which is a jump from the 18 that Baghdad initially planned to buy.

But even after the purchase goes through it would take years of training for the Iraqi Air Force to be able to protect its air space.