"This should be a moment of reconciliation not only in Iraq but in the international community," Mr Blair said in a speech on foreign policy at Georgetown University in Washington.
"The war split the world," he said. "The struggle of Iraqis for democracy should unite it."
He described Iraq's new government as a child democracy "struggling to be born" and the international community as "the midwives".
"You may not agree with original decision," Blair told his audience of some 800 students, faculty members and invited guests. "You may believe mistakes have been made. You may even think how can it be worth the sacrifice.
"But surely we must all accept this is a genuine attempt to run the race of liberty."
Mr Blair, who visited Iraq earlier this week, said that although the international community "can argue forever" on the merits of the 2003 US-led invasion to topple Saddam Hussein, he said it was time to move on and support the new government in Iraq.
"I don't want to reopen past arguments," he said, striking a conciliatory tone. "I want to advocate a new concord to displace the old contention."
Mr Blair was US President George W. Bush's staunchest ally in the run-up to the Iraq invasion in March 2003, but like Mr Bush he has seen his popularity tumble, largely because of the Iraq debacle.
Both men on Thursday admitted that mistakes had been made in Iraq, but refused to set a timetable for the withdrawal of their troops from the country.
The United States has some 133,000 soldiers in Iraq and Britain 8,000.
Mideast conflict
Mr Blair said though success in Iraq would reverberate across the Middle East, a more concerted and concentrated effort was needed throughout the region, especially in tackling the Israeli-Palestinian conflict and Iran's controversial nuclear program.
"I don't believe we will be secure unless Iran changes," he said.
He added that the international community would be "hugely empowered" in the Arab world if the Israeli-Palestinian conflict were resolved.
"This is a dispute which casts a shadow over all attempts at reconciliation," he said. "Under its cover, global terrorism recruits."
Mr Blair in his speech also called for an overhaul of international institutions such as the United Nations, the World Bank and the International Monetary Fund (IMF).
"A Security Council, which has France as a permanent member but not Germany, Britain but not Japan, China but not India, to say nothing of the absence of proper representation from Latin America or Africa, cannot be legitimate in the modern world," he said.
During his visit, Mr Blair and Mr Bush also announced they had resolved a long-running dispute over technology that had threatened to derail plans for development of a new Joint Strike Fighter aircraft.
US officials said the deal would allow the British to make their own adapations to the aircraft without having to call in US technicians.
Britain, angered by US reluctance to share the codes, had been prepared to cancel the planned purchase of 150 aircraft at 104 million dollars apiece.
Following his speech at Georgetown, Mr Blair had lunch with President Bush at the White House to continue discussions on Iraq and other issues.