He added: "Most people looking at Britain say we have taken the lead in the measures to prevent a global collapse."
On Tuesday, US President Barack Obama signed a $787bn economic stimulus package.
Several other countries have programmes in place.
Mr Brown said: "America has just announced the biggest fiscal and monetary stimulus in the history of its country.
"Every part of the world must be part of the stimulus to the economy, giving support into the economy with investment, getting interest rates down as much as possible, and I believe one of the features of our discussions at the G20 summit on 2 April is how all countries can come together to do that.
"Some may have to do more on interest rates; some may have to do more fiscal stimulus. The whole point of the G20 is that the world must take action to deal with a global problem."
He added: "The old orthodoxies will not serve us well in the future. We've got to think the previously unthinkable. We've got to do what was previously undoable.
"The co-operation that's needed around the world is not something that has been achieved before - but I believe it can be achieved to meet the needs of our times."
Following recent criticisms of the role of the Financial Services Authority in regulating UK banks, Mr Brown said: "I'm right, I think, to emphasise the international nature of the problem."
He also said the "biggest failure" was on a global level, but added: "Of course I accept there need to be changes in the UK system."
The prime minister brushed aside the suggestion that he was tempted to step down to become the "world's financial regulator".
He said: "There is no possibility anyway of a job called Global Financial Regulator. I want get on with the job I'm doing.
"My priority is to help people in this country who are facing problems with their mortgages, problems with their jobs and problems with small business finance."
But Mr Brown also spoke of his "regret" that he failed over the years to win support for changes to the international system of regulation in banking.
He said there had been a need for such reform for some time -- especially as banks had become more global - sometimes working in dozens of different countries, where there's different supervision.
"My regret is that I failed over these years to persuade people - with sufficient force - that our proposals should have been implemented after the Asian crisis. And I tried to persuade the other countries that this was an important issue.
"But, once the Asian crisis had gone, people's attention was on other things. And, then of course we had all the other issues at the beginning of the century related to terrorism. So, it's hardly surprising that people's attention was on other things."
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