John Prescott has insisted he is not going to "give in to the media campaign" and will remain in his job as deputy prime minister.
His comments came as the chairwoman of the parliamentary Labour party (PLP) called on backbenchers to support Mr Prescott.
Ann Clwyd said she would be "very sorry" to see him quit, telling Today: "Despite the criticism he should stay on. Hopefully he will stay on.
"I see the stories in the press. I know he's been pooh-poohed very vigorously, but these things tend to have a certain shelf life and then they go.
"And I am hoping that.the Labour party will be able to give him the necessary support so that he remains in office."
Speaking to this morning's The Independent, Mr Prescott made clear that he had the support of Tony Blair and insisted he had no intention of resigning.
"I am not going to give in to the media campaign. I am not going to resign. I am going to get on with my job," he said.
Mr Prescott has been under pressure to explain what he does to justify a £138,000 a year ministerial salary, after he was relieved of his departmental responsibilities following the cabinet reshuffle earlier this month.
The prime minister has publicly backed him, saying he played an important role in chairing cabinet committees and negotiating controversial proposals across government departments, but this has done little to fend off the critics.
Following the publication of a photograph of Mr Prescott playing croquet on Thursday afternoon, when he was supposed to be running the country in Mr Blair's absence, the knives have really come out.
A number of Labour backbenchers have lined up to criticise him, with at least two openly calling for him to quit. However, an equal number of cabinet ministers have appeared in public to insist he does a vital job and must stay.
One of the main concerns is that Mr Prescott, always a figure of fun, has become too much of a joke following his affair with his diary secretary to continue to hold such an important office as deputy prime minister.
Yesterday, the Conservatives revealed that he had broken his own department's handbook in conducting a relationship with Tracey Temple in his office, as it prohibits the "improper use" of furniture and workspace and discourages lewd behaviour.
"It comes as no surprise that a man who couldn't even pay his own council tax bill can't be bothered to read his own official handbook," said shadow local government minister Caroline Spelman.
"This just shows that there seems to be one rule for Labour ministers living it up at taxpayers' expense, and another for everyone else. Perhaps if John Prescott had read the rulebook, he wouldn't be where he is now."