During a television address to the nation from the Oval Office, Mr Bush called for American unity and a plea for support for the Iraq war.
"Whatever mistakes have been made in Iraq, the worst mistake would be to think that if we pulled out, the terrorists would leave us alone," Mr Bush said.
"The safety of America depends on the outcome of the battle in the streets of Baghdad," he said.
Criticised by some Democrats for not getting bin Laden when there was a chance in late 2001, Mr Bush renewed his pledge to track down the elusive spiritual leader of al-Qaeda.
"Osama bin Laden and other terrorists are still in hiding. Our message to them is clear: No matter how long it takes, America will find you, and we will bring you to justice," he said.
Bush approval plummets
Mr Bush spoke a day after The Washington Post reported that the search for bin Laden had gone "stone cold" with no credible leads in more than two years.
Bin Laden is believed to be hiding in the mountains along the Afghanistan-Pakistan border.
The September 11 crisis brought Americans together in remarkable political harmony behind their untested president.
But many parted ways with him when the Iraq war turned out to be far more costly in blood and money than forecast.
Today, Mr Bush's approval rating has plummeted and he is fighting to keep his Republicans from being ousted in November elections.
Mr Bush said the war on terrorism was only in its "early hours" and described it as a "struggle for civilisation."
"Our nation has endured trials -- and we face a difficult road ahead," the US President said.
"Winning this war will require the determined efforts of a unified country. So we must put aside our differences, and work together to meet the test that history has given us."
His argument for staying in Iraq amounted to the same theme he has been using on the campaign trail; that it would be wrong to give in to the temptation to pull out of Iraq before the government in Baghdad is stable, which many American increasingly see as a fleeting prospect.
"If we yield Iraq to men like bin Laden, our enemies will be emboldened. They will gain a new safe haven, and they will use Iraq's resources to fuel their extremist movement. We will not allow this to happen. America will stay in the fight," he said.
UN pays tribute
Meanwhile the United Nations has paid tribute to the nearly 3,000 people who died in the terrorist attacks against the United States on September 11, 2001, which Secretary-General Kofi Annan called "an attack on humanity itself".
General Assembly President Jan Eliasson spoke for the 192 nations in the world body when he paid homage "to all those who were victims on that dark day five years ago, and to the thousands and thousands of others who have been victims of terrorism all over the world".
Later, Mr Eliasson asked diplomats to stand for a moment of silence in memory of those who died, a gesture that was mirrored in the UN Security Council at the other end of the building.
Mr Annan said in a statement that "the attacks of September 11,
2001 cut us all to the core, for they were an attack on humanity itself".
He urged all UN member states to swiftly implement the UN Global
Counter-Terrorism Strategy adopted last Friday which "sends a clear message that terrorism is unacceptable, no matter who commits it, no matter what the reason".
The strategy calls on all governments to take concrete steps to prevent and combat terrorism in all forms and to address the conditions "conducive to the spread of terrorism," he said.