The US says it is considering a draft agreement with Iraq on the role of its troops there after the UN mandate for their presence expires later this year.
Details have not been released, but officials say it would see US combat forces withdrawn from Iraqi towns and cities by the middle of 2009.
The troops would withdraw completely from Iraq by the end of 2011, they add.
Defence Secretary Robert Gates has begun briefing key members of Congress, although their approval is not needed.
Secretary of State Condoleezza Rice is also said to be pressing Iraqi leaders to accept the deal.
On Wednesday, the Iraqi government said it was considering the draft because a compromise had been reached on the issue of immunity for US military personnel and contractors.
Any deal must be approved by the Iraqi cabinet, the three-man Presidency Council, and critically, by the Council of Representatives.
The current UN mandate for US-led coalition forces in Iraq expires on 31 December. About 144,000 of the 152,000 foreign troops deployed there are US military personnel.
The BBC's Richard Lister in Washington says major obstacles to an agreement on extending the mandate have included how long US troops would stay, and whether they would continue to be immune from prosecution in Iraq.
The Iraqi government has publicly insisted on a clear timeline for withdrawal, and US officials said the current draft included a timeline for US withdrawal before the end of 2011.
It is also said to grant Iraqi judicial authorities limited ability to try US troops and contractors for major crimes committed off-duty or off-base - and only then if a joint US-Iraqi committee agreed.
The government in Baghdad believes the current immunity from Iraqi prosecution by granted to US troops and contractors by the former Coalition Provisional Authority (CPA) undermines Iraqi sovereignty.
However, many members of Congress are concerned about allowing Iraq's judicial system to have even limited authority over US troops.
"I am sceptical of any agreement that would subject US servicemen and women to the jurisdiction of Iraqi courts in the middle of a chaotic war," Senator Carl Levin, chairman of the Senate Armed Services Committee, told the Associated Press.
A Pentagon spokesman said the administration was not concerned by the draft agreement and that Mr Gates was currently calling Congressional leaders to explain the details.
"I don't think the secretary would be making phone calls in support of the document if he didn't believe it adequately protected our forces in Iraq," Geoff Morrell said, adding that it included both combat and legal protections.
Our correspondent says the two sides have been close to a deal before, but the fact that the Bush administration is now briefing key members of Congress on the details of this document suggests the negotiations may now have run their course.
But as they are not required to formally endorse this agreement, the biggest question mark remains over whether the Iraqis will, he adds.
6 months ago