"The men and women of our military face a continuing risk of danger and sacrifice in Iraq," Mr. Bush said in his weekly radio address. But, he added, "our military is acting decisively against these threats." 

Mr. Bush raised the topic 10 weeks after Baghdad fell and 7 weeks after he declared on May 1, aboard the aircraft carrier Abraham Lincoln, that the active phase of the fighting was largely over. After coming under sporadic attacks since then, the military has mounted significant operations to round up suspected resisters. More than 28,000 troops are in Baghdad enforcing the law, he said. 

He avoided the lingering question of whether Saddam Hussein was alive or in any way coordinating the attacks, saying only that "dangerous pockets of the old regime remain loyal to it, and they, along with their terrorist allies, are behind deadly attacks designed to kill and intimidate coalition forces and innocent Iraqis." 

He also said the occupying forces would keep looking for chemical and biological weapons in Iraq, and defended the intelligence assessments before the war, saying that the intelligence services of "many nations" had similarly concluded that Mr. Hussein had illegal weapons.

White House officials said that amid continuing questions about the casualties and about Mr. Bush's remarks before the war on weapons of mass destruction, he felt he had to address what one official called "the growing questions about why we went in, and what we are doing there." 

Mr. Bush vowed to pursue evidence of those weapons, which has been scant, "no matter how long it takes." 

The nearly daily reports of attacks on American forces in Iraq have prompted questions on Capitol Hill and debate among political strategists about the public's patience for the military occupation of Iraq. 

Pentagon officials said on Friday that 55 Americans had died in Iraq since President Bush declared the end of major combat operations on May 1. Most died in accidents, and 18 in hostile fire. 

On Thursday, Paul T. Nakamura, a 21-year-old Army specialist, died when the vehicle he was traveling in was hit by a rocket-propelled grenade. 

A total of 138 Americans died in the offensive to capture Baghdad and topple Mr. Hussein, according to military officials. That puts the total American dead at 193. 

During the main military operations, the American military presence in Iraq reached a peak of 151,000; today that number is about 146,000. 

Mr. Bush briefly touched on the situation in Iraq in three appearances in the last week, telling cheering crowds that Mr. Hussein was no longer a threat to the United States. But he had not so specifically discussed the risk to American troops until today, and the radio address, officials say, is regarded inside the White House as the way for Mr. Bush to deliver the message with just the emphasis he seeks. 

He spent much of the brief address detailing $700 million in relief and reconstruction aid that the United States has spent, and said that "after years of neglect, Iraq's 4.2 million children under the age of 5 are receiving vaccinations against diseases such as polio, measles and tuberculosis." 

Mr. Bush did not detail the casualties that the United States has suffered as it deals with attacks by snipers, guerrillas and others hostile to the occupation. But while military commanders mourn the loss of each soldier, they also say that the attacks have been insignificant militarily and are having no effect on day-to-day operations of the American combat forces in Iraq. 

At the Pentagon, Defense Secretary Donald H. Rumsfeld expressed confidence this week in the public's patience, saying that the American people "have a very good center of gravity." 

The drumbeat of reports that American troops have come under attack in Iraq raises the possibility that, in an election year, a prolonged and painful occupation could hurt Mr. Bush. He is seen as having gained political support for his handling of the invasion of Iraq but is also being criticized for how things have gone since the main combat operations ended. 

But even a leading Democratic pollster said there was little indication of slipping public support. 

"If peace does not turn out as well as the war turned out, it could undermine how people evaluate this president's foreign policy skills and how they evaluate the war," said the pollster, Mark S. Mellman. 

"A long occupation that is difficult, daily headlines of American casualties, an unwelcome atmosphere for American troops or even a continued large American presence — eventually those kinds of things have the potential to undermine support for the policy and support for the president," he added.

But he also said that "the tide has not turned in the public's mind — it's a question of time and events — and that tide may never turn." 

While several commentators have said the public will take notice if the number of Americans killed in Iraq during the postwar period surpasses the wartime deaths, senior military officers say that sets a false comparison, because the allied force raced to Baghdad while suffering low casualties. 

Other issues that may affect public support for the reconstruction of Iraq are the debate over the administration's statements about chemical and biological weapons and how long a sizable American ground force will be needed to stabilize Iraq. Military officers acknowledge concerns over a single attack that kills or injures a large number of American forces, like the bombing of the Marine barracks in Beirut. 

Rich Bond, a former chairman of the Republican National Committee, said Democratic candidates who might be planning to criticize the Iraq mission from the campaign trail risked alienating voters. "Our men and women are under fire and dying to protect freedom," he said. "It demonstrates the huge disconnect between the liberals who control the Democratic Party and the rest of America." 

Unlike the war in Vietnam, in which public support for the conflict dwindled as combat deaths grew, the American people still view the Iraq offensive "as a just cause," Mr. Bond said. 

Mr. Rumsfeld likewise rejected predictions of slipping public support, and said at a Pentagon news conference this week: "I think the American people have a very good center of gravity. And I wouldn't sell them short, if I were you." 

The American people, Mr. Rumsfeld added, "recognize the difficulty of the task." 

On Capitol Hill, the Senate Armed Services Committee met in a closed-door session on Friday to review the security situation in Iraq. Afterward, Senator John W. Warner, the Virginia Republican who serves as chairman, said, "We're very concerned in our committee, as I find colleagues throughout the Senate are, as well." 

He also expressed "full confidence" in Gen. Tommy R. Franks, the wartime commander, and his forces "to bring about a greater degree of order in that nation," and he added: "This is not a risk-free operation. And we regrettably have to bear those risks to fulfill this mission."