President Bush, facing political pressure for troop cutbacks, said Tuesday he would make a fresh assessment about Iraq's needs for U.S. military help now that a new government has taken office in Baghdad.

Bush also said Americans should not judge what's happening in Iraq solely on the basis of the unrelenting violence. "It is a difficult task to stop suicide bombers," Bush said at a news conference.

Bush said progress was being achieved on the military and political fronts — as Iraqis are trained to handle their own security force and a new unity government begins works.

Iraq's government will assess its security needs and its security forces and work with U.S. commanders, Bush 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. "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."

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, and election-year pressure is building to begin troop withdrawals.

At least 40 people were killed Tuesday in attacks across Iraq. In Baghdad, a bomb exploded in the courtyard of a Shiite mosque and killed no fewer than 11 while wounding at least nine others.

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," the president said in the East Room, standing alongside Israeli Prime Minister Ehud Olmert.

"But that's the main weapon of the enemy, the capacity to destroy innocent life with a suicider," Bush said. "So I view progress as — is there a political process going forward that's convincing disaffected Sunnis, for example, to participate? 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.

"Trying to stop suiciders, which we're doing a pretty good job of on occasion, is difficult to do," he said.

Bush's comments came just hours after the White House had played down prospects of major troops withdrawals.

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

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 Pentagon indicated it may be too soon to make decisions on troop cuts.

"The conditions on the ground tell us that our job's not done," Snow said.

At the Pentagon, Brig. Gen. Carter Ham told reporters that he is unaware of any numerical target for troop cuts this year, and he cautioned against expecting major reductions before Iraqi troops show they can handle the insurgents.

"We want to do it as soon as we can, but you can't do it too fast," said Ham, who is deputy operations chief for the Joint Chiefs of Staff. He cautioned against "rushing to failure."

Ham also noted that security conditions have been deteriorating in the restive city of Ramadi, where U.S. officials are not even certain who the enemy is. Some officials say the Ramadi problem argues against early decisions to cut troop levels.

British Prime Minister Tony Blair, Bush's chief partner in Iraq, visited Baghdad on Monday and agreed with the country'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.

"We are there at the request and behest of the Iraqi government," Snow said. "We'll stay only as long as the Iraqi government wants us to stay there. But at this point, we are not going to harness ourself to an artificial timetable."

Blair will be in Washington for talks with 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.

In an interview with al-Arabiya, the pan-Arab satellite TV station, Secretary of State Condoleezza Rice indicated that no decision on troop reductions would be made until U.S. officials consulted further with Iraqi leaders.

"General Casey will sit down with the Iraqi military people, with Iraqi civilians, with Prime Minister Maliki himself to try and determine what needs to be done, what role we will play in the coalition forces, what role the Iraqis will play," Rice said. She referred to Gen. George Casey, the top U.S. commander in Iraq.