After 90 minutes of talks with the president, Mr Brown said the US deserved the support of Britain and the rest of the world in the measures it was taking as part of its economic rescue plan.
"America and Britain have always stood together as one in times of difficulty and challenging times, and I have told President Bush today that facing global turbulence Britain supports the US plan," he said.
"Whatever the details of it, it is the right thing to do."
He went on to say that stability was the "first duty" of government and that UK ministers were doing everything they could, including working with other countries, to resolve the financial crisis.
Mr Brown and Mr Bush also discussed Iraq, Afghanistan and Georgia as well as the Doha round of world trade talks at the White House.
On Thursday, the prime minister urged world leaders not to use the financial crisis as an excuse to abandon efforts against global poverty.
Mr Bush has proposed the US government take on the debts of struggling financial firms in an attempt to keep them afloat and also prevent a recession.
The prime minister said quick action was needed to stabilise the economic situation and that longer-term reforms to the world's financial system were also needed.
"While the problem comes out of America, it has consequences for all of us and every family will want to know that we are doing everything in our power to ensure that there is stability," he said.
Meanwhile, a survey of 1,012 people for BBC Two's Daily Politics show suggests 36% trust Mr Brown and Chancellor Alistair Darling most to steer the UK's economy through the downturn.
Some 30% opted for Conservative leader David Cameron and shadow chancellor George Osborne, while 5% chose Lib Dem leader Nick Clegg and Treasury spokesman Vince Cable.
The poll, conducted ComRes on 24th and 25 September, suggests that 24% of people do not know which party offers the best option on the economy.
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