Labour MPs and activists are being urged to rally round John Prescott amid continued questions about his future as deputy prime minister.
Ann Clwyd says she hopes the stories will die down
Ann Clwyd, chairman of the parliamentary Labour Party, says she hopes he will receive the "necessary support" to continue in office.
She spoke as Mr Prescott, who turns 68 on Wednesday, said he was determined to ride out the criticisms.
"I am not going to give in to the media campaign," he told The Independent.
"I am not going to resign. I am going to get on with my job."
On Wednesday, Mr Prescott visited a drug treatment programme in Worksop.
He promised he would use his chairmanship of Cabinet committees to find ways for the Home Office, Department of Health and other agencies to work together to overcome drug abuse.
Ms Clwyd, who is visiting Iraq for the first time since the inauguration of the new government, said she hoped the furore about Mr Prescott would die down.
He has been plagued by damaging headlines since admitting to an affair with a secretary. He later lost his department but kept his £133,000-a-year Cabinet salary and two grace-and-favour homes.
Ms Clwyd hoped Mr Prescott could stay on as deputy prime minister and deputy Labour leader.
"I worked in opposition very closely with John Prescott when I shadowed employment policy and I always found him a very good person to work with professionally," she told BBC Radio 4's Today programme.
"I would be very sorry to see John Prescott go. 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 John Prescott and the Labour Party will be able to give him the necessary support so that he remains in office."
Her comments came as some Labour MPs called for Mr Prescott to resign.
'Determined to stay'
Mr Prescott caused even more outrage after photographs of him playing croquet at his country retreat Dorneywood, Buckinghamshire, emerged shortly before he took over the reins from Mr Blair.
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
But Mr Prescott's biographer, Colin Brown, said Mr Blair had told the deputy prime minister they were "linked" and there was "no intention that they will go separately".
Mr Prescott's parliamentary aide - Labour MP Paul Clark - insisted the croquet game had been merely part of a departmental away day.
On Tuesday, 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.
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.
Labour MP Stephen Pound said voters had a negative image of Mr Prescott, whose "sell-by date is rapidly approaching".