Deputy Prime Minister John Prescott will only step down from the Cabinet when Tony Blair sets a date for his own retirement, his biographer has said.
Downing Street insists it has "full confidence" in Mr Prescott
Colin Brown said the prime minister had stressed that the pair were "linked" and there was "no intention that they will go separately".
The claims follow a weekend of stories and photos of Mr Prescott, who is standing in for Mr Blair while he away.
But Downing Street insisted it still had full confidence in Mr Prescott.
But some Labour MPs are still want Mr Prescott, who turns 68 on Wednesday, to resign.
Biographer and journalist Mr Brown, who spoke to Mr Prescott on Tuesday, said he was "angry with the way the press has treated him" but determined not to resign.
He told BBC News 24: "I think that the vacancy will only arise when they go together - the prime minister and the deputy.
"I know that Tony Blair has told the deputy prime minister that they are linked and I don't think there's any intention that they will go separately."
1999: As transport minister - already dubbed "two jags" - uses official car to go a few hundred yards to conference
2001: Punches an egg-throwing protester during the General Election campaign
2003: Appears to give journalists a V-sign outside Downing Street
2005: Local reporter says Mr Prescott told him to "bugger off" during an interview
April 2006: Admits to having had an affair with a secretary after newspaper revelations
May 2006: Stripped of his department in reshuffle, but keeps title, salary and perks
May 2006: Photos show him playing croquet at his country retreat while deputising as PM
The latest controversy follows photographs of Mr Prescott playing croquet at his country retreat Dorneywood, Buckinghamshire, shortly after taking over the reins from Mr Blair.
Mr Prescott was stripped of his department in Mr Blair's May reshuffle, but kept his salary and perks, sparking anger from opposition parties and some Labour figures.
Mr Brown said: "He wasn't running the country that day... The prime minister was still in charge of the country."
He said Mr Prescott felt that if press clamour forced him to give up Dorneywood it would be "salami slicing and what would be next?".
Mr Prescott's parliamentary aide - the Labour MP Paul Clark - insisted the croquet game had been merely part of a departmental away day to discuss the restructuring of his office.
The prime minister's official spokeswoman said Mr Blair "has absolute full confidence in the deputy prime minister", but would not comment on Mr Brown's claims.
She said Mr Prescott was in Whitehall chairing meetings on Tuesday and was coordinating the government's response to the Indonesian earthquake.
It is thought Mr Blair wants to avoid a deputy leadership election as it would inevitably be tied to his own future.
Senior Labour backbencher Ian Gibson said there was only a "50:50" chance of Mr Prescott still being in post by this time next week.
"What matters to the person in the street is what he is doing, what is his job," he told BBC News. "He has all the fringe benefits and so on, but yet it's not clear what his position is.
"I think that's what makes people cynical about politics, and John perhaps in particular."
Labour MP Stephen Pound said voters had a negative image of Mr Prescott, whose "sell-by date is rapidly approaching".
But Defence Secretary Des Browne said Mr Prescott was "a very valued colleague" who had "given a lifetime of service" to the Labour Party.
Ian MacKenzie, Mr Prescott's former special adviser, said his ex-boss was one of the hardest working ministers he knew.
"Anybody who's worked for him will tell you - trying to persuade him not to work a 16-hour day, a seven-day week and a 51-week year is very difficult indeed," he said.
Ex-minister Glenda Jackson also backed Mr Prescott, saying nobody had worked harder for the Labour government.