Brown has been prime minister for only a month, and there have been questions about whether he's as committed to success in Iraq as was his predecessor, Tony Blair.
Brown made it clear that his government isn't in a hurry to withdraw British forces from Iraq.
"The notion of America and Britain sharing values is very important, and that we have an obligation, it seems to me, to work for freedom and justice around the world," Bush said.
"In Iraq we have duties to discharge and responsibilities to keep in support of the democratically elected government and in support of the explicit will of the international community," Brown said.
Brown added that any decisions on force levels would be based solely on the advice of his military commanders in Iraq.
Britain now has 5,500 troops in Iraq and is shifting their mission from combat to helping Iraqi forces take over security responsibilities.
But at today's news conference, Brown and Bush promised that the efforts of both countries would be as strong as ever.
The two leaders said that during their talks over the last two days they agreed on a number of global issues in addition to Iraq. These included Iran, world trade, global climate change, and the crisis in Sudan's western province of Darfur.
Brown and Bush both said their agreement was based on their two countries' long alliance and shared values.
"I believe it's a partnership that's founded on more than common interests and more than just a common history," Brown told reporters today. "It's a partnership founded and driven forward by our shared values."
For his part, Bush said the two men got along so well that they had a two-hour discussion over dinner that resumed the next morning at breakfast. He called the conversation "relaxed" and "meaningful."
"The notion of America and Britain sharing values is very important, and that we have an obligation, it seems to me, to work for freedom and justice around the world," Bush said. "And I found a person who shares that vision and who understands the call. After all, we're writing the initial chapters of what I believe is a great ideological struggle between those of us who do believe in freedom and justice and human rights and human dignity, and cold-blooded killers who will kill innocent people to achieve their objectives."
'Use All Assets'
At one point, Brown defined terrorism as a "crime" that must be fought vigorously. Bush has disagreed with some U.S. and European officials who say fighting terrorism should not be a job for the military, but for police.
Bush was asked about this and replied that fighting terrorism requires all a nation's resources.
"We're dealing with a variety of methodologies to deal with [terrorists]," he said. "One is intelligence, one is law enforcement, and one is military. We've got to use all assets at our disposal to find them and bring them to justice before they hurt our people again. In the long run the way to defeat these people is through a competing ideology."
Brown was then asked if he shared Bush's view, and the prime minister replied, "Absolutely."
Bush, meanwhile, praised Brown's response to recent failed attacks in Britain.
Among the subjects they discussed during the talks was Iran. Many Western countries say Iran's nuclear-energy program is aimed at developing nuclear weapons. Iran says it is interested merely in nuclear energy.
Brown said he's satisfied with the way Europe and the United States have confronted Iran so far and promised more of the same in the near future. The British leader said the UN sanctions already in place are working, and that he's ready to impose even tougher sanctions, again through the United Nations.