Cabinet ministers have rallied around the prime minister after Clare Short said he should quit.
Claire Short warns 'a big, nasty split' within Labour
In an interview broadcast on Sunday, Ms Short called for Mr Blair to stand down as Labour leader before things get "even nastier".
But Trade and Industry Secretary Patricia Hewitt said Mr Blair was "the most successful
leader of the British Labour Party that there has ever been".
Home Secretary David Blunkett weighed in too, voicing exasperation at what he described as efforts to "plot" to remove Mr Blair.
"Clare Short is being typically self-indulgent. It is important to get behind the prime minister and focus on the things that matter to people, like decent opportunities and economic prosperity," he said.
And Transport Secretary Alistair Darling told BBC One's Breakfast with Frost: "She has said it before and I don't think it has any support."
He warned that Ms Short was in danger of "downgrading" her achievements in office.
Speaking in an interview for GMTV's Sunday Programme, Ms Short said the trade unions were unhappy and the degree of trust for Mr Blair in the country had fallen.
She warned of "a big nasty split" that would damage Labour if Mr Blair stayed.
"I think it would be in the interests of Tony Blair himself and his legacy of the Labour Party, and actually of the country, if he would think of making a voluntary departure and we could have an elegant handover and Labour could renew itself in power," she said.
Mr Darling accepted that the government was facing "a bit of turbulence" amid the rows over Iraq and foundation hospitals and had to fight for the trust of voters.
Darling admits government is facing 'turbulence'
He went on: "I think by the
time of the next election people will see what we have delivered on the public
"They will have a choice between us and whether or not they want
Iain Duncan Smith and his crew back in.
"I think trust is something you have got to work for, you have got to build,
but frankly I don't think Clare's contribution is going to help one way or the
Mrs Hewitt echoed that sentiment on BBC Radio 4's The World this Weekend.
She went on: "Trust is an issue, trust is something we have to work for in government every day that we are in office.
"I think that the way that we go on building and rebuilding trust is by getting back to our absolutely basic values. Because those are the values of the
vast majority of the British people."
On Iraq, Ms Short accused Mr Blair of leading Britain into the conflict on the basis of "half truths" and "slight deceptions".
She accused the prime minister as seeing himself as "a kind of higher mortal than the rest of us" when he was taking decisions on Iraq.
"I'm sure he's convinced that what he did was right but I'm also sure that he fooled the country in a series of ways in a way that's intolerable when it's a matter of war and peace and human beings' lives and the future of a country," she said.
She also rounded on plans for foundation hospitals and student top-up fees, which she described respectively as a
"complete mess", and an "outrageous and absolutely crummy" policy.
Ms Short denied she is plotting for Gordon Brown to take over as Labour leader.
But she said Mr Blair had caused a "great big division" with No 11 over the euro.
In a separate interview for the Sunday Telegraph, Ms Short also said: "I am not just saying it to carp against Tony - this is serious. It is our country, it is our constitutional system. I am not angry. I am sad."