But he said: "The issue is, can we deal with these three fundamental problems?
"I believe that you do need the global action that we are talking about and I believe that the British economy, under the leadership, taking these difficult decisions about how we can get through it, is in better position than most economies."
He said it was essential that summits, like the G8, helped create global solutions to the world's dependence on oil and increase food production.
Asked whether he would step down as Labour leader, if he became a liability to the party, Mr Brown said: "If I thought I wasn't the right person I wouldn't have stood for leader - the test of leadership is taking people through difficult times."
He added: "I think I'm the right person to take people through these difficult times."
The prime minister is being credited behind the scenes with ensuring that the G8 did not backslide on its commitments to African development
Mr Brown's leadership could be put under pressure if Labour is defeated in the previously safe Glasgow East seat in a by-election on 24 July.
The party is still reeling from losing its Crewe and Nantwich seat to the Tories at a by-election and coming fifth in the Henley by-election.
Business minister Baroness Vadera rejected the British Chambers of Commerce suggestion that Britain was verging on recession.
She told BBC Radio 4's The World At One: "Indeed, 27 out of 27 independent forecasters wouldn't agree for this year, and for next year 26 out of 27 independent forecasters would not agree.
"They all agree that we are going to have growth but we are going to have a downturn."
But the Conservative former chancellor Ken Clarke told the BBC he was less optimistic than Mr Brown.
"I'm afraid the British economy is one of the badly exposed ones," he said.
"And now our housing market is going off a cliff that's going to affect consumer spending and a very domestic British situation is going to emerge, in which, because of recent events, [Britain] is going to be one of the more affected countries of the western world."
Among other issues on the agenda at the G8 were sanctions against Robert Mugabe's regime in Zimbabwe - including calling for a UN envoy to be sent there to broker a deal.
And Mr Brown said he was pleased aid promises for Africa, which were made at the Gleneagles summit in 2005, would be retained.
World leaders agreed to stick to a 2005 pledge to double aid by 2010, despite fears over the credit crunch.
The G8 announced a multi-billion pound investment in malaria nets, fighting infectious diseases and education in developing countries.
"We are delivering everything we promised; other countries will do the same," said Mr Brown.
"Ten million children will go to school. Malaria nets will save thousands and more healthcare. These are big concrete changes."
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