The White House on Tuesday played down prospects of major troop withdrawals from Iraq in the near future.

"We're not going to sort of look at our watches and say, oop, time to go," presidential spokesman Tony Snow said.

The establishment of a unity government in Baghdad has stirred talk of troops reductions by the United States and Britain, the two major players in terms of soldiers in Iraq.

British Prime Minister Tony Blair, Bush's chief partner in Iraq, visited Iraq on Monday and agreed with Iraq's new leadership that Iraqi forces would start assuming full responsibility for some provinces and cities next month, beginning a process leading to the eventual withdrawal of all coalition forces.

British media quoted an unidentified senior British official traveling with Blair as saying coalition forces should be out within four years. Blair and Iraqi Prime Minister Nouri al-Maliki declined to set a timetable for that withdrawal.

Blair will be in Washington for talks with President Bush on Thursday and Friday about Iraq and other subjects, such as the impasse with Iran over its nuclear program and the deteriorating prospects for peace in the Middle East.

The United States has about 132,000 troops are now in Iraq; Britain has about 8,000.

"As we've said all along, when Iraq stands up, we'll stand down," Snow said. "And whether that fits into any convenient time frame, we're going to find out. The conditions on the ground are going to determine when the United States begins doing troop withdrawals and that sort of thing. And that, and that alone, is going to be the ultimate factor.

"We're not going to sort of look at our watches and say, oop, time to go, because that would be irresponsible," Snow said. "The most important thing to do is to make sure that we have laid the basis for a successful, self-governing, peaceful and stable Iraq."

Defense Secretary Donald H. Rumsfeld is holding three days of meetings at the Pentagon this week with the heads of all the major war-fighting commands, including Gen. John Abizaid, the Central Command chief whose area of responsibility includes Iraq and Afghanistan. These are regularly scheduled meetings -- held about every three months -- that focus more on long-range concerns and policies than on issues like U.S. troop levels in Iraq.

Rumsfeld, at a Senate hearing last week, was pressed to say whether the American public could be assured of a major U.S. troop withdrawal by year's end.

"I can't promise it," Rumsfeld said, adding that he nonetheless is hopeful that it will happen.

Gen. Peter Pace, the chairman of the Joint Chiefs of Staff, who also testified, was asked whether U.S. troops could withdraw completely from any of Iraq's 18 provinces within the next three months.

"No, sir," Pace replied.