WASHINGTON -- President Bush has agreed to set a "general time horizon" for deeper U.S. troop cuts in Iraq, the White House said yesterday. It's a dramatic shift from his once-ironclad unwillingness to talk about any kind of deadline or timetable.

The announcement 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 Democratic-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 unpopular war.

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

Bush and Iraqi Prime Minister Nouri al-Maliki talked about the stalled negotiations during a secure video conference on 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 U.S. troop cutbacks.

The White House statement was intentionally vague and did not specify what kind of timelines 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 on 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."

Democratic Rep. Bill Delahunt of Massachusetts, who has led House hearings on the planned agreement with Iraq, said the "time horizon" cited by the White House was "very vague and nebulous." He also said the agreement taking shape seemed "far less grandiose than what was initially articulated."

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.

So far, the United States has handed control of 10 of 18 provinces to Iraqi officials.

"Obviously, if Iraqis are assuming more missions, then you need less American troops," Johndroe said.

A major troop buildup ordered by Bush in January 2007 has ended. In recent days, the 3rd Infantry Division's 2nd Brigade, the last of the five additional combat brigades sent in last year, left the country. There are still 150,000 U.S. troops in Iraq -- as many as 15,000 more than before the buildup began.

Defense Secretary Robert Gates said officials are looking for ways to send additional U.S. troops to Afghanistan this year.