Bush, in his first prime-time news conference, said the United States would "reconsider" its current military campaign against Afghanistan if the Taliban government were immediately to "cough ... up" bin Laden and others in the al-Qaida terror network.
But the president also looked ahead to a post-Taliban Afghanistan, in which the U.S. government would participate in a nation-building chore that he has insisted his administration did not wish to perform.
Bush touched on a number of related points during a 45-minute session with reporters in the East Room at the White House, exactly one month after the terrorist attack on New York and the Pentagon and only hours after the FBI issued a new warning of possible terrorist activity against Americans in coming days. Among the highlights, Bush:
"We shouldn't play favorites" he said.
Bush said that "all interested parties" should have an opportunity to take part in creating an Afghanistan that was not a safe haven for terrorists.
It would be "a useful function for the United Nations to take over the so-called 'nation-building' -- I would call it the 'stabilization' -- of a future government after our military mission is complete," Bush said. "We'll participate. Other countries will participate."
Bush addressed the considerable image-building task facing the United States as it attempts to convince Muslims and others around the globe that the war on terrorism is not a war on Islam.
"I am amazed that there is such misunderstanding of what our country is about, that people would hate us," he said. "We've got to do a better job of making our case."
Administration officials have warned that the United States needs to avoid personalizing the war on terrorism into a Bush-bin Laden clash.
The president tried to make the point again that his target is the entire al-Qaida network, not just bin Laden.
But he could not avoid direct references, often pointed, to the Saudi exile. He referred to him both as "Mr. bin Laden" and "the evil one."
"We'll smoke him out of his cave, and we'll get him eventually," Bush said.
He said the FBI was working to ensure that any al-Qaida members in the United States are brought to justice. But as if to underscore the enormity of the task, Bush said that al-Qaida operates "in roughly 68 countries."
"We must rid the world of terrorists so our children and grandchildren can grow up in freedom," he said. "It is essential. It is now our time to act."
In responding to reporters' questions, Bush was careful not to trip over the diplomatically sensitive aspects of the campaign against terror.
He mentioned Syria, a nation on the U.S. list of terrorist sponsors, as a possible ally, praising that government's statements about helping.
And in an apparent reference to countries, such as Egypt and Saudi Arabia, that have been criticized for not doing enough, Bush said, "Any help is better than no help. We're very appreciative of the help we are getting."
But the president also portrayed himself as someone with little patience for diplomatic niceties and mere words.
"I'm more interested in action and results. And if you want to join the campaign against terror," he said to other countries, "all I ask is results."
Referring to the effort to cut off the flow of funding to al-Qaida and other terrorist organizations, Bush said, "If you say you want to join us to cut off money, show us the money. If you say you want to join us militarily, like Great Britain does, do so."
Asked if Afghanistan might become a Vietnam-like quagmire for the United States, Bush said the country had learned some "very important lessons" in Vietnam.
"Baby boomers such as myself were used to getting caught in a quagmire of Vietnam, where politics made decisions more than the military sometime," he said. "This is a different kind of war that requires a different type of approach and a different type of mentality."
Bush also said that Americans had learned "a good lesson" Sept. 11, "that there is evil in this world."
He called on parents to tell their children "we love them, and there is love in the world, but also remind them there are evil people."
After fielding 14 questions, Bush concluded with an appeal to the children of the United States to donate $1 each to a special relief effort to be overseen by the Red Cross.
He said donations should be sent to America's Fund for Afghan Children, in care of the White House, 1600 Pennsylvania Ave., Washington, D.C. 20500.
The evening marked the first time Bush has held a news conference in the elegant East Room, where presidents have often appeared on such occasions.
Bush has preferred the less formal trappings of the White House briefing room, where he has held three question-and-answer sessions with reporters since taking office.
Bush's job approval ratings hovered just above 50 percent before the terrorist attacks, but his standing in the polls has soared to 90 percent or above, a level approached in recent years only by his father during the Persian Gulf war in 1991.
The last time a president held a prime-time news conference was April 1995, when Bill Clinton met reporters in the East Room -- the night before the bombing of the federal building in Oklahoma City.
Last night's event was covered by all the major broadcast networks, except for the WB network and UPN, which showed WWF professional wrestling.
Earlier, after a meeting with his Cabinet, Bush encouraged Congress to act on his energy package, one of many administration initiatives that have received little attention since the attacks.
He has spent much of his time at a secure and undisclosed location away from the White House since last weekend -- a reminder of the extraordinary security precautions in effect.
Bush was asked last night about those steps, which have been taken at the same time the administration is trying to convince Americans that the country is safe and people should go about their normal routines.
Bush said that it was necessary to separate the president and vice president "for the sake of continuity of our government" but added he had met with Cheney yesterday in the Oval Office.
"I was pleased to see him. He's looking swell," Bush said to laughter from the correspondents.