The announcement yesterday put Bush in the position of offering to talk with Iraqi leaders about a politically charged issue that he adamantly has refused to discuss with the Democrat-led Congress at home. It also could complicate the presidential campaign arguments of Republican John McCain and Democrat Barack Obama, who have staked out starkly opposite stands about the war.

What has changed? The sharp reduction in violence in Iraq, to the lowest level in four years, has made the country's leaders increasingly confident and more assertive about its sovereignty, giving rise to demands for a specific plan for U.S. forces to leave.

Iraq has leverage because the White House is struggling to salvage negotiations for a long-term agreement covering U.S. military operations there. The White House said its goal is to conclude that deal by the end of this month.

Bush and Iraqi Prime Minister Nouri al-Maliki talked about the stalled negotiations during a secure video conference Thursday, agreeing "on a common way forward to conclude these negotiations as soon as possible," a White House statement said.

The two leaders agreed that improvements in security should allow for the negotiations "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 U.S. combat forces from Iraq," the White House said.

Bush repeatedly has vetoed legislation approved by Congress setting deadlines for American troop cutbacks.

Yesterday's White House statement was intentionally vague and did not specify what kind of time lines were envisioned. That allows Iraqi officials, who are facing elections in the fall, to argue they are not beholden to Washington or willing to tolerate a permanent military presence in Iraq. For Bush, it points the way toward a legal framework for keeping American troops in Iraq after a U.N. mandate expires Dec. 31.

"The agreement will look at goal dates for transition of responsibilities and missions," said Gordon Johndroe, spokesman for Bush's National Security Council. "The focus is on the Iraqi assumption of missions, not on what troop levels will be."

As for the campaign to elect a new president, McCain firmly opposes any withdrawal timetable, while Obama pledges to pull out combat troops within 16 months. By talking about a "time horizon," Bush appeared at odds with McCain and could make his own GOP administration a tougher target for Obama's antiwar barbs.

McCain issued a statement saying: "Progress between the United States and Iraq on a time horizon for American troop presence is further evidence that the surge has succeeded. . . . If we had followed Sen. Obama's policy, Iraq would have descended into chaos, American casualties would be far higher, and the region would be destabilized."

Ben Rose, a senior adviser to Obama, said: "It's another indication that the administration is moving toward . . . Sen. Obama's position on negotiating the removal of our forces as part of our ongoing discussions with the Iraqi government."

House Speaker Nancy Pelosi (D., Calif.) said Bush was not going far enough. "After rejecting 18 months of attempts by the Democratic majority in Congress to adopt redeployment timetables, the president now proposes a vague general time horizon that falls far short of a commitment to ending our involvement in Iraq," she said.

Rep. William Delahunt (D., Mass.), who has led House hearings on the planned agreement with Iraq, said the "time horizon" cited by the White House was "very vague."

Iraq has proposed requiring U.S. forces to fully withdraw five years after the Iraqis take the lead on security nationwide - though that condition could take years to meet.