"Our nation has endured trials, and we face a difficult road ahead. Winning this war will require the determined efforts of a unified country," he said in a prime time television and radio address.
"So we must put aside our differences, and work together to meet the test that history has given us," the president said.
Earlier he had visited each of the three sites tied to the September 11, 2001 strikes.
Mr Bush has waged an aggressive public relations offensive aimed at blunting anger over the unpopular Iraq war two months before November elections that some in his Republican party worry may cost them control of the US Congress.
The president, in a series of speeches, has sought to place the situation in Iraq in the context of the global war on terrorism, which he launched after the attacks five years ago.
"This struggle has been called a clash of civilisations. In truth, it is a struggle for civilisation. We are fighting to maintain the way of life enjoyed by free nations," Mr Bush said in the address.
"America did not ask for this war, and every American wishes it were over.
So do I. But the war is not over, and it will not be over until either we or
the extremists emerge victorious," he said.
Mr Bush rejected calls for setting a timetable for a US withdrawal from Iraq
and vowed to bring bin Laden to justice.
"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," Mr Bush said.
Fifth anniversary marked
Earlier Americans paused in silent tributes to mourn the nearly 3,000 victims of the September 11 attacks.
Solemn ceremonies in New York highlighted a day of commemorations.
Families and friends of those killed began gathering around dawn at the gaping hole in lower Manhattan where the Twin Towers once stood to read the names of the 2,749 people who perished there.
A hush fell over Ground Zero as a minute of silence was observed at 8:46 am (2246 AEST), the moment when a hijacked plane slammed into the first of the Twin Towers.
Accompanied by a solo cello, emotional families, some clutching photographs of their loved ones, read the names and lay floral tributes in the reflecting pools that stand in the construction site.
President Bush joined the tributes to those killed in New York, Washington and Pennsylvania.
Mr Bush marked a moment of silence at a fire station on New York's Lower East Side, paying tribute to 343 fire-fighters killed.
He then flew to Pennsylvania, where United Airlines Flight 93 went down, killing 40 people, after a struggle between the hijackers and passengers.
"We celebrate the victory they won here in the first battle in America's war on terrorism," General Tommy Franks, retired commander of US troops in Iraq and Afghanistan, said at the Pennsylvania ceremony.
Vice President Dick Cheney and Defence Secretary Donald Rumsfeld, architects of a US-led offensives in Afghanistan and Iraq, attended a memorial ceremony at the Pentagon, where 189 people died.
World reaction
As US allies expressed solidarity with Washington in the fight against terror, newspapers around the world criticised the US decision to invade Iraq and the conduct of the US-led campaign against Islamic extremism.
In Kabul, Afghan President Hamid Karzai thanked the United States for its help in ousting the Taliban and called on the world to "continue the fight against the menace of terrorism with greater resolve and dedication."
German Chancellor Angela Merkel warned that human rights must be respected in the fight against terrorism.
"Our battle against Islamic terrorism will only succeed if we strengthen democratic and economic development in crisis regions and cultivate respect for human rights," she said in a statement.
Saudi Arabia voiced sympathy with the American people on the anniversary of the attacks, but warned against attributing terrorism to Islam. Fifteen of the 19 suicide hijackers were Saudis.
In Australia, Prime Minister John Howard urged moderate Muslims to be more critical of terrorism. "We shouldn't pussyfoot around. No decent, genuine Muslim would support terrorism," he told The Australian newspaper.
At the United Nations, UN chief Kofi Annan and the Security Council paused for a minute of silence in tribute to the victims.
"The attacks of September 2001 cut us all to the core, for they were an attack on humanity itself," Mr Annan said in a statement.
Chinese state media, however, dwelled more on the American response to the atrocity.
"It's fair to say that September 11 changed the United States. But what really changed the world was the erroneous US response ... especially the war in Iraq," an editorial in the People's Daily said.
Many Arab newspapers said the US-led "war on terror" and invasion of Iraq had pushed the world closer to a clash of civilisations between the West and the Muslim world.
"The administration of George W. Bush used a vengeful mentality in dealing with the 9/11 crime and has turned the entire world into a battle ground," said the independent Al-Ghad daily in Jordan.
And a reminder that al-Qaeda, blamed for the September 11 attacks, remained a threat came just hours ahead of Monday's ceremonies when Osama bin Laden’s deputy Zawahiri warned that the Gulf and Israel would be the next targets.
"We have repeatedly warned you and repeatedly offered a truce with you, and so we now have all legal and rational justification to continue to fight you until your power is destroyed or you give in and surrender," Zawahiri said in a message to Western powers in his latest video.