Mr Brown said he wanted to help "hard-pressed families"
Gordon Brown has said he is "determined" to lead Labour into the the next general election, insisting the party is on course for victory.
Labour won just 16% of the vote in the European Parliament elections, finishing in third place.
But Mr Brown told the News of the World: "We must and we will win."
In a Guardian interview on Saturday, the prime minister admitted recent political events had made him think he could "walk away from this tomorrow".
'Trappings of power'
As well as humiliating poll results, the prime minister has faced a failed backbench plot to oust him, a string of resignations from his government and public anger over MPs' expenses.
Mr Brown told the News of the World he was not interested in power for its own sake but said he believed he still had an unfinished task to complete.
He said: "It is because of my purpose in politics that I am determined to lead Labour to the next general election.
"I think people want to work for a common purpose and I think it's really important that, when things are difficult, we show that we can come through."
"It has never been the trappings of power I care about but what we can do in power to help hard-pressed families."
Mr Brown urged MPs to spend the summer in their constituencies, speaking to voters and rebuilding trust.
In Saturday's Guardian, Mr Brown admitted that leaving office "would probably be good for my children" but insisted Labour could win under his leadership.