Bush said finding him and thwarting his plans are "the greatest challenge of our day."
He highlighted the urgency, saying: "Recently we learned that Osama bin Laden has urged the [Iraq-based suspected] terrorist [Abu Mus'ab al-] Zarqawi to form a group to conduct attacks outside Iraq, including here in the United States. We're on a constant hunt for bin Laden. We're keeping the pressure on him, keeping him in hiding. And today Zarqawi understands that coalition and Iraqi troops are on a constant hunt for him as well."
But the hunt for bin Laden so far has been fruitless. Two months ago, General Pervez Musharraf, the president of Pakistan, said his trail had "gone cold." And on 1 March, General John Abizaid, the man in charge of the U.S. part of the search, cautioned Congress that success is not guaranteed.
Kenneth Allard says he wholeheartedly agrees with Abizaid's assessment. Allard, a retired U.S. Army colonel who served as an intelligence officer, tells RFE/RL that a manhunt is not the right job for an army.
"Military forces typically do not engage in the apprehension of individuals," Allard says. "Our stock in trade is taking down a regime. It's like looking for individual grains of sand, when your objective is to shovel out a foundation. We do a great job of foundation digging. We don't do a very good job of finding an individual grains with names on them."
But Allard says it is likely that U.S. special forces and paramilitary personnel of the Central Intelligence Agency (CIA), are part of the search. He says they are trained not to fight pitched battles, but to undertake missions like the hunt for bin Laden, and are prepared to fight only in emergencies.
The next question, Allard says, is what happens if bin Laden is eventually captured? He says if bin Laden is killed, many Muslims probably would revere him as a martyr. If he is captured alive, he could speak at his trial to rally his fellow militants.
Either way, according to Allard, Americans can expect bin Laden's followers to mount vengeance strikes in the United States.
But Allard says this probably would leave Americans no more vulnerable to attack than they are now. And he adds that failing to capture bin Laden is not an option, and that the United States is better off if bin Laden is dead.
"I would much rather have the dead Osama as a potential martyr than a live Osama running around right now," Allard says. "Because the most powerful symbol that he exerts to his followers is that he has been able to defy the United States. He's been able to pull off [the attacks of 11 September 2001] and effectively get away with it. Symbols really matter."
But symbols have limited value, according to Nathan Brown, who specializes in Middle Eastern affairs at the Carnegie Endowment for International Peace, a private policy-research center in Washington.
Brown points out that the United States is not just fighting Al-Qaeda but many additional groups with at best only a loose affiliation with bin Laden's organization. Now that bin Laden has inspired them, he says, they can act autonomously.
"Capturing or killing [bin Laden] wouldn't end the problem that he's come to symbolize," Brown says. "What he managed to do was to get disparate groups together and get them to focus on attacking Western targets rather than their own governments. But it's unclear that he's really knitted those disparate groups into one single movement. And so cutting it off at the top is not going to completely end what those various groups do."
Brown says he prefers to sidestep the question whether the United States would benefit more from a dead bin Laden than a living one. Instead, he says: "Putting [bin Laden] on trial raises all kinds of difficult issues, because you are giving him a platform by which he can address his various constituencies. And he can speak fairly effectively to those constituencies. So in a sense, a trial would be a very mixed blessing for the United States."
Brown says that while he expects capturing bin Laden would have no immediate effect, it might pay off in the long term. It could discourage some young Muslim men from joining militant groups.