BAGHDAD — Iraq and America are near an agreement on all American combat troops leaving Iraq by October 2010, with the last soldiers out three years after that, two Iraqi officials told the Associated Press on yesterday. American officials, however, insisted no dates had been agreed.

The proposed agreement calls for Americans to hand over parts of Baghdad’s Green Zone — where the American Embassy is located — to the Iraqis by the end of 2008. It would also remove American forces from Iraqi cities by June 30, 2009, according to the two senior officials, both close to Prime Minister Maliki and familiar with the negotiations.

The officials, who spoke separately on condition of anonymity because the talks are ongoing, said all American combat troops would leave Iraq by October 2010, with the remaining support personnel gone “around 2013.” The schedule could be amended if both sides agree — a face-saving escape clause that would extend the presence of American forces if security conditions warrant it.

American acceptance of a specific timeline would represent a reversal of American policy in place since the war began in March 2003. Both Iraqi and American officials agreed that the deal is not final and that a major unresolved issue is the American demand for immunity for American soldiers from prosecution under Iraqi law.

Throughout the conflict, President Bush steadfastly refused to accept any timetable for bringing American troops home. Last month, however, Messrs. Bush and Maliki agreed to set a “general time horizon” for ending the American mission.

Mr. Bush’s shift to a timeline was seen as a move to speed agreement on a security pact governing American military presence in Iraq after the U.N. mandate expires at the end of the year.