Bush is reflecting the precarious political and military situation he faces. He repeatedly has said that any public timetable for a withdrawal would only help the enemy. But elections are six months away and a majority of Americans say in surveys that they want fewer U.S. soldiers in Iraq.

Bush said the swearing-in of a new government in Iraq over the weekend has opened a door for change. The new Iraqi leaders will assess the country's security needs and forces, then work with U.S. commanders, he said.

"We haven't gotten to the point yet where the new government is sitting down with our commanders to come up with a joint way forward," the president said Tuesday. "However, having said that, this is a new chapter in our relationship. In other words, we're now able to take a new assessment about the needs necessary for the Iraqis."

Bush spoke in response to a question about whether he is confident he can start withdrawing troops at the end of the year. He did not give a direct answer to the question, raised at a press conference with Israeli Prime Minister Ehud Olmert, but signaled that change is coming.

He used similar language in Chicago on Monday, when he gave his first speech since the new government was sworn in over the weekend.

"As the new Iraqi government grows in confidence and capability, America will play an increasingly supporting role," Bush said during that address.

Pressed Tuesday on how he can expect Iraqis to bring down the violence when the most powerful military in the world has not been able to, Bush suggested that reducing the suicide bombings that have terrorized the country will not be the main factor for bringing U.S. troops home.

"It is a difficult task to stop suicide bombers," Bush said.

"So I view progress as: Is there a political process going forward that's convincing disaffected Sunnis, for example, to participate?" the president asked. "Is there a unity government that says it's best for all of us to work together to achieve a common objective, which is democracy? Are we able to meet the needs of the 12 million people that defied the car bombers? To me, that's success."

And he made it clear that stopping many of the suicide bombers ultimately will be a problem for Iraqis, although the United States still is helping and "we're doing a pretty good job of it, on occasion."

"What the Iraqis are going to have to eventually do is convince those who are conducting suiciders who are not inspired by al-Qaida, for example, to realize there is a peaceful tomorrow," Bush said. "And those who are being inspired by al-Qaida, we're just going to have to stay on the hunt and bring al-Qaida to justice. And our army can do that and is doing that right now."

Iraq hangs heavily over Bush's presidency. More than 2,450 members of the U.S. military have died since Bush ordered an invasion of Iraq more than three years ago. The war is a major factor in Bush's slump in the polls to the lowest point of his presidency. There are 132,000 U.S. troops in Iraq.

At least 40 people were killed Tuesday in attacks across Iraq. In Baghdad, a bomb exploded in the courtyard of a Shiite mosque, killing at least 11 and wounding at least nine.

Bush said Americans should look beyond the daily scenes of violence.

"If one were to measure progress on the number of suiciders, if that's your definition of success, I think it obscures the steady, incremental march toward democracy we're seeing," he said.

The establishment of a unity government in Baghdad has stirred talk of troop reductions by the United States and Britain, the two major players in terms of soldiers in Iraq. But with violence still widespread, both the White House and the Pentagon indicated it may be too soon to make decisions on troop cuts.

"We're not going to sort of look at our watches and say, 'Oop, time to go,"' said spokesman Tony Snow. "The conditions on the ground tell us that our job's not done."

Iraq tops the agenda when British Prime Minister Tony Blair is in Washington for talks with Bush on Thursday and Friday.