UK Prime Minister Tony Blair and US President George W Bush have made a stark public acknowledgement that they made mistakes in Iraq.
Mr Bush said the biggest US error was the prison abuse scandal in Abu Ghraib, which it was now paying for.
The two leaders have never admitted their mistakes in such frank terms, the BBC's Jonathan Beale says.
They also called for the international community to give its full support to the new Iraqi government.
In a Washington news conference, the British prime minister said it was important to Iraq's leaders to know that "we will stand firm with them" against "terrorism and violence".
The talks in Washington also focused on Iran, with Mr Bush offering rewards for Tehran if it ends uranium enrichment.
Both men have seen their popularity drop and are keen to ensure a positive legacy as their terms draw to a close, correspondents say.
BBC diplomatic correspondent Jonathan Marcus says Iraq has cast a shadow over the leaders' careers and both were seeking to play up the potential for change afforded by the new democratically-elected government in Baghdad.
Asked about mistakes in Iraq, Mr Bush brought up the prisoner abuse scandal at Baghdad's Abu Ghraib prison.
"We've been paying for that for a long period of time," he said.
He also said he regretted having used unsophisticated language such as "Wanted dead or alive", which had been misinterpreted in some parts of the world.
The BBC's Jonathan Beale in Washington says the US president was full of introspection after frequently being criticised for lacking powers of self-analysis.
Mr Blair, who held talks with new Iraqi Prime Minister Nouri Maliki in Baghdad this week, was also prepared to acknowledge errors, accepting that the exclusion of all of Saddam Hussein's Baath party members from leadership roles may have only fuelled the insurgency.
But both men remained convinced that they had done the right thing in Iraq.
Mr Blair said: "I came away thinking the challenge is still immense, but I also came away thinking more certain than ever that we should rise to it."
That challenge, he said, was "daunting... but inspiring".
Whatever people's misgivings about the 2003 invasion of Iraq, he said, "our duty, but also the duty of the whole international community, is to get behind this government and support it".
However, neither man would set a timetable for the withdrawal of troops from Iraq.
They also discussed Iran's nuclear programme, and its refusal to suspend uranium enrichment. The US suspects Iran of seeking nuclear weapons, although Tehran says its work is for peaceful, energy purposes.
Both leaders refused to outline a timetable for withdrawing troops
Mr Bush said the US would continue to work with Iran's government despite its "intransigence" but urged it to suspend enrichment to avoid international isolation.
The leaders meet again on Friday after Mr Blair's foreign policy speech at Georgetown University.
In his speech, the UK leader is expected to focus on the values of democracy and reform of the post-World War II institutions, such as the UN and International Monetary Fund.
Mr Blair has pledged to resign before his third term ends, which will be in May 2010 at the latest. Mr Bush leaves office in 2009.
The prime minister was given wholehearted support by the president, however. Asked by a journalist what Mr Bush wanted to see in Mr Blair's successor, Mr Bush replied: "I want him to be here so long as I'm president."