Tony Blair has privately told John Prescott that they are "linked" and will go together when the Prime Minister decides to step down.
Mr Blair made it clear during a conversation in recent days he did not want the Deputy Prime Minister to resign in spite of the pressure on him from some Labour MPs for keeping his "perks" and his £133,000 salary while losing his Whitehall department.
"I am not going to give in to the media campaign," Mr Prescott told The Independent. "I am not going to resign. I am going to get on with my job."
Mr Prescott has discussed with a close circle of friends the possibility of giving up Dorneywood, his grace-and-favour home, to end the damaging attacks on him. However, he has ruled out the option, saying it would open him to "salami slicing" by his critics, who would then call for other "perks", such as his ministerial flat in Admiralty House, to be given up.
Mr Blair, who has left Mr Prescott in charge of the Government while he is on holiday in Italy, authorised Downing Street to issue a statement yesterday giving total backing to Mr Prescott. Downing Street said the Prime Minister had "absolute full confidence" in his deputy. A spokeswoman said: "They stay in contact regularly."
No 10 released details of Mr Prescott's diary for the week to underline his workload in Mr Blair's absence.
It said he was chairing meetings with officials, including discussions with the Department for International Development on how to respond to the Indonesian earthquake. Mr Prescott later visited the Indonesian Embassy to sign a book of condolence for its victims.
Later this week the Deputy Prime Minister will visit a drug rehabilitation project and will represent the Government in a discussion at the British Irish Council on climate change. At the weekend, he will fly to Canada for a conference on the environment.
The Labour MP Glenda Jackson, a former minister in Mr Prescott's department, also came to his aid by rebutting calls by other female Labour MPs for him to resign because of his affair with his diary secretary.
"I find it incredibly patronising to be told that women choose to cast their votes based exclusively on the private life of male MPs," Ms Jackson said. "There is no one who has worked harder for the Labour Party and the Blair Government than John Prescott."
Mr Prescott said the renewed storm over his cabinet role was started because of the campaigns being mounted at Westminster to succeed him. He said he understood potential candidates jockeying for position because he had done the same when he won the deputy leadership.
There is a belief at Westminster that Mr Blair will step down early next year. Canvassing has started among Labour MPs for support for a number of ministers who are believed to be ready to run for the deputy leadership, including Harriet Harman, Alan Johnson, Peter Hain and Jack Straw.
Some Blairites fear that if Mr Prescott stood down before Mr Blair it would trigger in-fighting between Brownites and Blairites. However, the Brown camp suspect that some in Downing Street have been trying to force Mr Prescott to quit to refresh the Government with a new deputy and buy Mr Blair more time.
The Defence Secretary, Des Browne, acknowledged that Mr Prescott had been "damaged" by the exposure of his affair, but backed him to stay.
However, Labour backbench critics kept up the pressure for him to go. Ian Gibson, a Labour MP, told BBC Radio 4's Today programme that the photographs of Mr Prescott playing croquet at Dorneywood did "not amount to that much". He added: "What matters to the person in the street is what he is doing, what is his job. He has all the fringe benefits and so on but it's not clear what his position is. That's what makes people cynical about politics and John in particular."
Mr Prescott faced further embarrassment over the publication of the staff handbook from the Office of the Deputy Prime Minister. It warns against "improper" conduct during work hours. His former diary secretary, Tracey Temple, has claimed their affair was carried out in his office and grace-and-favour flat in Admiralty House, Whitehall.
Caroline Spelman, the shadow local government minister, said: "Perhaps if John Prescott had read the rule book, he wouldn't be where he is now."