Subject to final approval by the top Iraqi leadership, the exit date for U.S. troops would be December 2011, although the Americans insist on linking that target to additional security and political progress.
President Bush has long resisted a timetable for pulling out, even under heavy pressure from a nation distressed by American deaths and discouraged by the length of the war that began in 2003. But that has softened in recent weeks.
The timing has major political importance in both Iraq and the United States.
The two contenders to replace Bush as commander in chief, Republican John McCain and Democrat Barack Obama, spar almost daily over the future course of the war.
Obama wants all U.S. combat forces out of Iraq within 16 months of his taking office, saying they are needed more urgently in Afghanistan. McCain says recent security improvements in Iraq show that decisions on the timing of further pullouts should be determined by circumstances on the ground rather than by prearranged timetables - a position the White House has vigorously held until recently.
The administration has inched toward the Iraqi view that setting at least a target date for withdrawal would make it politically palatable for Iraq's government to accept a substantial U.S. troop presence beyond this year.
The rationale for the pullout is that Iraqi security forces will be ready to stand on their own, although it remains possible that some U.S. military training role would continue. In Iraq, provincial elections are supposed to be held later this year, followed by national balloting in 2009.
In one key part of the draft agreement, private U.S. contractors would be subject to Iraqi law, unlike at present, but the American side held firm in its insistence that U.S. troops would remain subject exclusively to U.S. legal jurisdiction, officials said.
There is an additional sense of urgency to complete a deal because the U.N. Security Council resolution that sets the legal basis for the U.S. troop presence in Iraq is due to expire at the end of this year.
Asked about withdrawal, Secretary of State Condoleezza Rice, said Thursday in Baghdad, "We have agreed that some goals, some aspirational timetables for how that might unfold are well worth having in such an agreement." Her use of the term "aspirational" suggested that the timetables would be linked in some undisclosed way to the attainment of measurable progress in the security, political and perhaps economic fields.
Other U.S. officials said the deal includes agreement that by June 30, 2009, U.S. combat forces would be out of Iraq's cities, set up elsewhere in the country in what the military calls an overwatch role - available to assist Iraqi security forces as needed, while continuing to train and advise Iraqi troops.
At a joint news conference, Rice and Foreign Minister Hoshyar Zebari said the two sides had accepted the draft agreement and would await a review by Prime Minister Nouri al-Maliki and other top Iraqi leaders - some of whom oppose some parts of the deal - as well as the Iraqi parliament. The next step is consideration by al-Maliki and his executive council Friday.
In the Sadr City section of eastern Baghdad, more than 500 followers of the anti-American Shiite cleric Muqtada al-Sadr held a rally Thursday evening to denounce the Rice visit and the proposed security arrangement. Marchers carried flags and al-Sadr's picture, chanting, "No to the agreement."
Saleh al-Mutlaq, leader of the second-largest Sunni faction in parliament, issued a statement saying the Americans should not depend on any agreement signed with the Shiite-dominated government. He called on the government to put the deal to a popular referendum rather than simply submit it to parliament.
U.S. officials in Washington, speaking on condition of anonymity because the deal is not final, said Bush administration acceptance of the arrangements was not in doubt unless Iraqi leaders insisted on changes. The administration has pledged to inform Congress but not submit the agreement for formal approval.
In Baghdad, Rice met with Zebari, al-Maliki and other officials on a brief visit intended to push the Iraqis toward agreement.
Said Zebari: "This agreement determines the principal provisions, requirements to regulate the temporary presence and the time horizon, the mission, of U.S. forces."
Bush has stood firmly behind al-Maliki, and the U.S. resisted pressure last year from its Sunni Arab allies elsewhere in the Middle East to dump the Shiite prime minister in favor of a more secular leader.
But al-Maliki has apparently taken a tough stand in the negotiations to refurbish his nationalist credentials and avoid the label of "America's man" ahead of coming elections.
The Shiite political establishment is also anxious to run the country without U.S. constraints, believing it has the right as leaders of Iraq's largest community, which had been marginalized politically since the modern Iraqi state was established following the collapse of the Ottoman Empire after World War I.
Rice spoke optimistically of completing a deal but stressed that it still needed top-level Iraqi approval. She also said it was made possible by security improvements.
"I have to say, if I could just make the point, the reason we are where we are going, talking about this kind of agreement, is that the surge worked, Iraqi forces have demonstrated that they are strong and getting stronger," she said.
Zebari, asked about fears expressed by neighboring countries over such a pact, said in Arabic: "This decision (agreement) is a sovereign one and Iran and other neighboring countries have the right to ask for clarifications ... There are clear articles (that) say that Iraq will not be used as a launching pad for any aggressive acts against neighboring countries and we already did clarify this."
A State Department transcript of Zebari's remarks said he added that Iran had been advised of that provision.
In other developments: