Mr Bush praised Mr Brown for the UK's battle against terrorism
Mr Brown said both nations had duties and responsibilities in Iraq, and that he would seek military advice before announcing any changes in policy.
The pair met at Camp David, near Washington, amid widespread interest about whether they could work together.
The talks also focused on Afghanistan, Darfur, world trade and climate change.
Ahead of the summit there was speculation about whether the Texan president and the Scottish prime minister would find some common ground.
In the event, Mr Bush spoke warmly of the "special relationship" with the UK, describing it as "our most important bilateral relationship" - the same term used by Mr Brown ahead of his trip to the US.
Britain and America's policies on Iraq are in step - for now, at least
BBC political editor Nick Robinson
Read Nick's thoughts in full
The president said he found Mr Brown a warm, humorous man, far removed from the "dour Scotsman" image sometimes portrayed by the media.
He also paid tribute to Mr Brown's personal strength in overcoming the death of his first child in 2002.
And he joked when he learned that six of Mr Brown's newly-appointed cabinet were under 40 years old, telling the prime minister: "You must be feeling old."
But the BBC's political editor Nick Robinson, at Camp David, says Mr Brown did nothing to return those personal compliments - even referring to their meetings as full and frank, which is normal diplomatic code for an argument.
Iraq debate
On Iraq, Mr Brown said any recommendation on the future role of the UK's 5,500 troops in Iraq could be put to parliament after British MPs return to work in October after a summer break.
That would leave any decision on UK troop levels until after a final report on the US "surge" in Iraq by Mr Bush's commander in Iraq, General David Petraeus.
The consequences of failure would be disaster for Great Britain and the US, something this Prime Minister understands
George W Bush
US President
"Our aim, like the United States is, step-by-step, to move control to the Iraqi authorities," Mr Brown said.
Mr Bush then linked the fortunes of both nations to the outcome of events in Iraq.
"The consequences of failure would be disaster for Great Britain and the US, something this prime minister understands," the president said.
'Common struggle'
Mr Brown, who faced a series of attempted bombings in the UK in the days after he assumed office in June, denounced terrorism as a crime, not a cause.
Correspondents say Mr Bush used familiar language, including soaring rhetoric on the subject of good and evil, while Gordon Brown was much more specific, detailing a long list of what the two men had talked about.
However, Mr Brown denied suggestions that his view of terrorism differed greatly from that of Mr Bush.
"We know we are in a common struggle, we know we have to work together, and we know we have to deal with it," he said.
"Today in 2007 we see the challenges are radically different to 10 years ago," Mr Brown added, citing climate change, Africa, and the search for a Middle East peace process as key issues.
He said both men had agreed on the need for tougher sanctions against Iran, and the importance of restarting the Doha round of world trade talks.
__NOTOC__President George W. Bush and Prime Minister Gordon Brown of the United Kingdom, walk past an honor guard Sunday, July 29, 2007

United Kingdom Prime Minister Gordon Brown met United States President George W. Bush at Camp David in Maryland for their first formal talks since Brown took office in June.

Gordon Brown arrived at Camp David on Sunday, July 30. Monday, they addressed the press in a joint press conference. According to reports, the talks focused on Iraq, Afghanistan, Darfur, world trade and climate change, amid speculation whether the two leaders could work together. Correspondents say they appeared relaxed as they faced reporters after their talks.


 
Both reiterated a commitment to fighting terrorism, which Prime Minister Brown called "a crime against humanity", and discussed ways of making sure that the two countries' security systems are "properly aligned" and share information.

President Bush spoke of waging an ideological struggle between those who "believe in freedom and justice and human rights and human dignity, and cold-blooded killers who will kill innocent people to achieve their objectives" and said that defending the "young democracies" of Afghanistan and Iraq was a way to defeat "an ideology of darkness" with a "more hopeful ideology". 

"It's very important for us to make it clear to those who are in harm's way that these missions will be driven not by local politics but by conditions on the ground," the President added.