The agreement, announced by both the White House and the Iraqi Government of Prime Minister Nuri Kamal al-Maliki, reflects a significant shift in the war in Iraq, reports the New York Times. The American military presence now depends significantly, if not completely, on Iraqi acquiescence, adds the paper.
The White House, however, has offered no specifics about how far off any "time horizon" would be, with officials saying details remained to be negotiated.
White House spokesman, Gordon D Johndroe said through a statement that the two leaders "agreed that improving conditions should allow for the agreements now under negotiation to include a general time horizon for meeting aspirational goals such as the resumption of Iraqi security control in their cities and provinces and the further reduction of US combat forces from Iraq."
The announcement came on the eve of a trip to Iraq and Afghanistan by the presumptive Democratic presidential nominee, Senator Barack Obama, who has vowed to pursue a strict phased timetable for withdrawing most combat troops from Iraq over 16 months beginning next year. He has cited Iraq's eagerness for a timetable as support for his strategy.
Obama's spokesman Bill Burton called the announcement "a step in the right direction," but derided what he called the vagueness of the White House commitment.
Senator John McCain, the Republican presidential candidate, praised the agreement as evidence that Bush's strategy of sending additional forces last year had worked and he sought to use it as a cudgel against Mr. Obama.
Nearly 140,000 American troops are still in Iraq, battling to restore that country to some sort of normalcy and democratic rule after over five years of conflict.
Some officials have said publicly that Iraq can take charge of much of its security by 2009, and be able to operate without American help by 2012.
Iraqi legislators have welcomed Friday's announcement, describing it as fundamental to an accord.
As one Bush Administration official was quoted by the NYT as saying: "We're converging on an agreement."
The agreement that American and Iraqi negotiators are now completing is more modest than the long-term strategic pact that both Bush and Maliki pledged last November to negotiate to replace the United Nations mandate at the end of this year.
The administration dropped a promise in that initial agreement to provide long-term security for Iraq, something that would require a treaty and Congressional approval. It has also backed off other demands for sweeping powers to continue military operations there indefinitely.
The negotiations have also been bogged down by issues involving the laws governing American troops, diplomats and civilian contractors, as well as details like customs duties and drivers' licenses for American soldiers.
Administration officials now say that they are negotiating an agreement that would establish the legal authority for American commanders to conduct combat operations, control airspace and detain Iraqi prisoners, while deferring the more complicated details of a "status of forces agreement" to the next administration.