Tony Blair has praised Gordon Brown as a "brilliant chancellor" - but has refused to endorse him as the next prime minister.
Blair has said he is "up for" the next election
Instead Mr Blair spelled out his own determination to lead the country into the next general election.
Speaking to BBC's Breakfast with Frost, the prime minister dismissed talk of his stepping aside in favour of Mr Brown as "decisions for the future".
But he conceded: "In the end, the British people are the boss - they're the people who make the decision.
"The reason that I'm up for it [leading Labour into the next election] is there's a lot more still to do."
Last week Deputy Prime Minister John Prescott suggested Mr Blair could "follow the example of Harold Wilson", who stood down mid-term.
He said Mr Blair would have Labour's full support if he led the party into the next general election, but hinted that the prime minister could be derailed by "events".
The remark followed his earlier comments, which had suggested cabinet ministers were jockeying for position in case Mr Blair stood down.
But the prime minister made it clear on Sunday that he intended to fight the next election as Labour leader.
"I am absolutely up for it ... You have always got to have the support of your party, but I believe I have that support. You have got to have the support of the people and that's decided in an election."
Mr Blair said the reason he seemed "unnaturally coy" about his future intentions was that whatever he said, it would either be construed that he was quitting or he was going to go "on and on and on".
Asked by Sir David Frost if he would endorse Gordon Brown as his successor, Mr Blair said: "These are decisions for the future, but I have always made it clear the high regard I have had for him.
"It's been a great partnership - he's a brilliant chancellor. He's delivered huge economic strengths to this country.
"He's a tremendous asset to the party and the country."
'Shadow of Iraq'
Mr Blair's comments came after a YouGov poll of 2,131 people published by the Daily Telegraph on Saturday suggested more voters believed that Gordon Brown would make a better prime minister.
A total of 29% plumped for the Chancellor as the ideal candidate, while 25% opted for Mr Blair.
The poll also said 59% believed that Mr Blair should resign immediately or before the next general election - with 41% wanting him to step down immediately and 18% preferring him to leave sometime ahead of the election.
Only 18% wanted him to stay for many more years.
Mr Blair said winning round public opinion did "get more difficult as you go on as prime minister" and conceded that Iraq was a divisive issue and a "shadow over our support".
But he insisted that people also recognised the government's other achievements in the economy, jobs, schools, the health service and policing.
Mr Blair defended his government's role in tackling obesity, following a report by the Commons heath committee that criticised ministers, the NHS, food manufacturers and advertisers for not doing enough to address the problem.
The prime minister said that while the government could encourage sport in school and food manufacturers to behave responsibly, individuals also had to play their part.
"I am responsible for many things, but I can't make people slimmer," he said.
"The prime responsibility for people looking after themselves is with people.
"But ultimately I think it is quite important we don't end up thinking the government can somehow determine whether people are large or small."