He rejected as "defeatist" a suggestion there was little he could do to influence rising oil prices and other global trends.
"I actually believe that there is a great deal you can do. Good economic decisions can help people through difficult times," he added.
On Wednesday, Mr Brown set out his draft legislative programme for next year - a list of bills that he plans to bring into Parliament from November this year.
But the announcement was overshadowed by a raft of gloomy economic news and the governor of the Bank of England Mervyn King warning the "nice" decade was over.
The Conservatives and Lib Dems said the government's programme was an exercise in political survival after Labour's local elections losses.
All parties are campaigning in Crewe and Nantwich ahead of the by-election on 22 May, which is seen as a key to Labour's prospects of recovery, after its worst local election results in 40 years.
The prime minister is also under pressure to explain a surprise £2.7bn tax cut package unveiled on Tuesday, after earlier insisting there was no cash for such a move.
In an interview with BBC Radio 4's Today programme, he insisted the tax cuts were not a short-term "fix" to get him out of political trouble, as other countries were also pumping money into their economies to ward off recession.
He denied he had caved in to pressure from his own MPs angry at the abolition of the 10p tax rate and said it was "absolute nonsense" to suggest, as former minister Stephen Byers did, that it showed he lacked a "strategic and principled" vision on tax and was just taking decisions for short-term advantage.
He also denied he had broken his own financial rules on only borrowing for investment, saying that applied to the entire economic cycle.
And he attempted to brush off criticism of his leadership style in memoirs by John Prescott and Cherie Blair, saying he did not listen to "innuendo and gossip".
He told interviewer John Humphrys he believed he was still the right person to steer the country through tough economic times, as he had done in his previous role as chancellor.
"I have had experience in the last 11 years of building a strong economy. I think few people would deny that we have had a good economy over the last 11 years.
"The reason it's going wrong are international factors that we are going to deal with and I am probably best placed to deal with these issues because of what I know about dealing with other countries on oil and other issues and we are going to keep going."
He said his priorities were oil prices, food prices, the housing market and "getting funds to business".
The UK was better placed to deal with worldwide recession than in the previous downturn under a Conservative government in the early 1990s, because of Labour's record on controlling inflation and maintaining high levels of employment, he added.
Mr Brown also rejected Conservative claims he had broken his own "sustainable investment" rule, which says debt must be kept below 40% of GDP.
He said the government had met both this rule and the "only borrow to invest" golden rule over the most recent economic cycle, which he said had lasted from 1997 to 2007.
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