He added: "We should be vigilant in maintaining the proactive approach to monetary and fiscal policy to enable our economies to resume their paths of upward growth.
"We want all our international partners to do the same, to ensure greater confidence in the financial system."
The two leaders also discussed Iraq, Zimbabwe, Afghanistan and Iran.
Mr Brown said the world owed Mr Bush a "huge debt of gratitude" for leading the fight against terror.
Mr Bush said: "We appreciate the special relationship with Britain."
Earlier, Mr Brown met Barack Obama - the Democrat front-runner in the race to become the party's presidential candidate - and his rival, Hillary Clinton.
He also held talks with Republican contender John McCain.
After the discussions, at the British embassy in Washington, the prime minister said: "I am absolutely confident that, having talked to the three candidates, that the special relationship between our two countries is strong and secure and valued by all of them.
"I am also absolutely confident that, through working with any of them, we could rise to the great challenges of the future."
During his visit to the US, Mr Brown has been pressing for international action to require banks to reveal how much money they have lost in the ongoing credit crisis.
He believes global economic confidence has a better chance of being restored if financial institutions own up to the full extent of their losses.
Shadow Foreign Secretary William Hague told the BBC that Mr Brown should adopt a "solid, not slavish" relationship with the US and the real test would be on "issues of substance - like how to deal with Iran's nuclear programme".
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