Former Home Secretary Charles Clarke has accused Gordon Brown of "absolutely stupid" behaviour during the furore over Tony Blair's leadership.
Mr Brown was pictured grinning as he left Downing Street
People were angry at photos of Mr Brown smiling broadly amid the chaos, Mr Clarke told London's Evening Standard.
Mr Brown should have stopped the plots against Mr Blair and still had to prove he was fit to govern, argued Mr Clarke.
Brown supporting MP John McFall accused Mr Clarke of a "mixture of hubris and a plea for recognition".
And former minister Glenda Jackson said the party would be watching to see whether Mr Blair distanced himself from Mr Clarke's comments.
She told GMTV: "Charles Clarke's comments seem to prove what everybody has long feared - that there are people close to the prime minister who would prefer to see David Cameron as prime minister rather than Gordon Brown."
Minister Harriet Harman said: "It's time now for everybody to shut up and focus on what we're in government and we're in the Labour Party to do."
Trade and Industry Secretary Alistair Darling later called for a "period of silence" from Labour MPs.
He told Channel 4 News he thought it "absolute nonsense" to suggest Mr Brown had damaged his reputation and his chances of becoming prime minister through his actions over the past few days.
Mr Brown ignored reporters' questions as he arrived to make a speech about Britishness in Edinburgh to kick off Labour's campaign for next May's Scottish elections.
But any hopes Mr Blair's announcement on Thursday that he would quit within a year would end Labour's hostilities appear to have been shattered by Mr Clarke's intervention.
The former home secretary said Mr Brown should have reined in the backbench rebels who sparked the latest leadership crisis by calling for the prime minister to quit immediately.
"What he should have done was come out strongly and distance himself from them," Mr Clarke told the Evening Standard.
"He could have done that with a click of his fingers. This has been complete madness."
Mr Brown met Tony Blair on Wednesday after a string of government resignations.
It prompted speculation the pair had reached a handover deal when Mr Brown was pictured grinning as he drove away from Downing Street.
Mr Clarke said: "A lot of people are very upset and cross about that. It was absolutely stupid, a stupid, stupid thing to do."
He said Mr Brown must "prove his fitness" to be prime minister.
"Part of the problem is that he lacks confidence. He is nervous," he said.
"That could all change when the burden of waiting for the job is lifted from his shoulders and I think it probably will. But the problem is, nobody really knows.
"He is not where he should be at the moment. He is talented and brilliant but there are these little incidences like the grin in the car that build up a terrible picture."
Mr Clarke said ex-Health Secretary Alan Milburn, a close Blair ally who has suggested he might stand for the top job, was "leadership material".
Former minister Frank Field also said Mr Brown "could have stopped the near destruction of the government if he had wanted but didn't".
Mr Field argued a leadership contest was needed to "test" the chancellor and he suggested Cabinet ministers John Reid and Alan Johnson could be candidates.
This view was echoed former government whip Graham Stringer, who said it was "disrespectful to the electorate" for Mr Blair and Mr Brown to decide the future of the country in a "private conversation".
"I hope Alan Johnson and John Reid will throw their hat into the ring for the good of the party and for the good of the country," he told BBC News 24.
The chancellor has insisted there are no "private arrangements" between himself and the prime minister and says it is to Mr Blair to decide when he goes.
Mr Brown used an article in the Sun newspaper to praise Mr Blair's "courageous" leadership.