Cabinet ministers have urged Tony Blair to stay on as prime minister and leave on his terms, rather than being forced out over the cash-for-honours inquiry.
Ms Jowell said Mr Blair should be allowed 'to get on with the job'
Culture Secretary Tessa Jowell said he should be allowed to "get on with the job". Health Secretary Patricia Hewitt urged him to "go in his own time".
Ms Jowell said people should be wary of "unattributed" stories suggesting Labour MPs wanted Mr Blair to go now.
The Tories say the uncertainty over his departure is paralysing government.
Mr Blair is due to stand down this year but has come under pressure to go now after being interviewed by police as a witness for a second time in the cash-for-honours inquiry.
And there have been reports that even Cabinet ministers are questioning how long Mr Blair can remain in his post.
But Ms Jowell, a staunch ally of Mr Blair, told the BBC's AM programme there was no evidence that MPs wanted anything other than for the government to get on with the job and for Mr Blair to go "in his own time".
Asked whether he should just go now, she added: "No I don't think so. He's made his intentions absolutely clear and I think he should be allowed to get on with the job."
'Presumption of guilt'
Ms Jowell said it would be a "presumption of guilt" if Mr Blair were to resign before the police inquiry was completed.
Labour Party chair Hazel Blears told GMTV that the media attention around the inquiry had overshadowed "quite a lot of our domestic agenda", but she did not think people were on tenterhooks waiting for Tony Blair to announce his resignation.
Government Chief Whip Jacqui Smith said it would be "undemocratic" to drive him from office during the inquiry.
Mrs Hewitt said there was "no sign of paralysis in the health service", adding: "Of course, the whole issue of the investigation, the allegations that are being made, of course that is damaging.
"But that is not a reason for the prime minister to be bundled out of office. The prime minister is giving outstanding leadership."
Four members of Mr Blair's inner circle, including his chief fundraiser Lord Levy, have now been questioned by police investigating claims that the honours were given in exchange for cash. All deny any wrongdoing.
Mr Blair was interviewed for a second time on Friday, 26 January, but the news was kept secret until last Thursday at the police's request.
He was not interviewed under caution, which means he is being treated as a witness rather than a suspect.
But some senior Labour figures have said the affair is damaging the government's reputation and eroding trust in politics.
And the Conservatives say uncertainty about Mr Blair's successor has left the government in paralysis.
On Sunday, Shadow Defence Secretary Liam Fox told GMTV that Mr Blair's authority was "ebbing away".
"I think it is not in the national interest for the prime minister to carry on. I think his continuation in office is an act of selfishness of historic proportions," he said.