In an interview with BBC One's Andrew Marr Show, Mr Brown, who is in Manchester for the Labour Party conference, said the best way to deal with the "economic storm" was to face it, and "demonstrate judgement and demonstrate wisdom".
Asked if his cabinet was behind him, he said: "I think we have a pretty united cabinet. I think people in the Labour Party want the cabinet to work together to deal with the economic problems we face."
He accused the Conservatives of being "pessimistic" about Britain and said on decisions from nationalising Northern Rock to a temporary ban on short selling - where traders bet on share prices falling - the government had got it right and they had been wrong.
But asked if he had made mistakes, he said yes, adding: "I always want to do better, and I will do better because we are dealing with the challenges that I think we are dealing with [them] in the right way."
He also told the programme he was a "pretty ordinary guy" - but said 10 years at the Treasury meant he was best qualified to deal with the international financial crisis.
He said the problems could not be dealt with through soundbites and slogans but through "wisdom" and "big decisions".
The PM looked more relaxed than in previous TV interviews. Perhaps he feels the immediate threat to his position has eased?
But he added he was "never complacent" and "always wanted to test what we have done against what has been done previously and learn lessons from that".
Thirteen Labour rebels - including David Cairns who stepped down as Scotland Office minister last week - have publicly called for a leadership challenge following disappointing by-election results and polls suggesting the Conservatives' lead is growing.
Labour MP Dr Ian Gibson told the BBC's Westminster Hour on Radio 4 that he was worried that if Mr Brown did not do a "humdinger" of a speech on Tuesday and did not get the support of the public and the activists, then "it could be curtains for him".
He said he did not think the time was right for a leadership challenge but everything depended on how he performed on Tuesday.
The most recent surveys suggest a mixed picture for the Labour Party.
An internet survey of almost 35,000 voters over 238 marginal seats for PoliticsHome.com, taken over three months up to the eve of the conference, projects a landslide victory for Conservative leader David Cameron at the next general election.
But a ComRes survey of 1,014 adults over two days for the Independent on Sunday suggested the Lib Dems had eaten into the Conservatives' lead and put the Lib Dems on 21%, Labour on 27% and the Tories on 39%.
Meanwhile a YouGov survey of 1,200 Labour members for the Sunday Times suggested 53% thought Mr Brown was "indecisive and dithering" and just 34% thought he had an exciting vision for the future.
During the interview Mr Brown also re-iterated his calls for global regulation of the financial markets and said he had been in touch with other world leaders on the issue this week.
And he said an element of the bonus system for City traders was "unacceptable" and, while it would be difficult to legislate against them in a global market, the Financial Services Authority was looking at the issue.
In an interview with the Sunday Telegraph he also pledged a free nursery place for every two-year-old as part of proposals for a major expansion of childcare over ten years.
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