Followers of Shiite cleric Muqtada al-Sadr demonstrate Thursday in Najaf, Iraq, against the visit of Condoleezza Rice to Baghdad. Iraq and the U.S. have reached a preliminary agreement to withdraw U.S. forces from Iraqi cities by next June, Iraqi Foreign Minister Hoshyar Zebari said Thursday after meeting with Rice.

Baghdad ? Iraq and the U.S. pushed close to a deal Thursday setting a course for American combat troops to pull out of major Iraqi cities by next June, with a broader withdrawal from the long and costly war by 2011.

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.

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.

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.

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.

The Iraqis are also reluctant to allow U.S. military contractors free rein when outside U.S. bases and without any Iraqi legal authority over them, according to a senior U.S. official who spoke on condition of anonymity.

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.”