President George W. Bush and British Prime Minister Gordon Brown are emphasizing common ground following talks at Camp David - the US presidential retreat outside Washington.
It was the first meeting between the two men since Mr. Brown took office last month.
The US and British leaders appeared relaxed as they faced reporters after their talks.
They stressed relations between the two countries are strong, despite the change at the top of the British government and strong public pressure in Britain to get out of Iraq.
Britain has been America's closest ally throughout the Iraq war. And Mr. Brown's predecessor - Tony Blair - was chastised at home for his close ties with the Bush administration.
Gordon Brown said the 5,500 British troops will stay in Iraq until their mission is complete.
"In Iraq, we have duties to discharge and responsibilities to keep."
He said the United States and Britain want to create conditions where the Iraqis can take control.
Mr. Brown noted British forces have already moved from combat to - what he called - an "overwatch" role in three of the four provinces where they have security responsibilities.
"We intend to move to 'overwatch' in the fourth province and that decision will be made on the military advice of our commanders on the ground."
His comments were in line with those made repeatedly in recent months by President Bush - that decisions on US troop levels are dependent on the situation in Iraq.
The president stressed he is waiting for a report to Congress in mid-September by US Commander in Iraq General David Petraeus before ordering any changes or modifications in strategy. When asked if he thought the war would continue through next year's US presidential election campaign and past the inauguration of his successor in January 2009, Mr. Bush hinted that may well be the case.
"I have said this is going to take a long time in Iraq, just like the ideological struggle (against extremists) is going to take a long time."
President Bush made clear that he believes Britain remains committed to the struggle in Iraq. He said Gordon Brown understands all that is at stake.
"There is no doubt in my mind that Gordon Brown understands that failure in Iraq would be a disaster for the security of our own countries."
In his comments after the talks - and in an opinion article printed in the Washington Post - Prime Minster Brown spoke of the unique partnership between the United States and Britain on all sorts of global problems. He said this relationship is founded on more than just common interests and common history.
"It is a partnership founded and driven forward by our shared values - what Winston Churchill, who was the first British prime minister to visit Camp David, called 'the joint inheritance of liberty, a belief in opportunity for all, a belief in the dignity of every human being."
The talks at the presidential retreat focused on a wide range of issues besides Iraq. They included the situation in Darfur, how best to revive the current round of world trade talks, and diplomatic efforts to keep Iran from acquiring the technology needed for nuclear weapons.
After a final luncheon session with President Bush and top aides, Mr. Brown was scheduled to stop in Washington to consult with congressional leaders. Before returning to London, he will travel on to New York where he will deliver a speech at the United Nations and meet with Secretary-General Ban Ki-moon.