John Prescott has accused former Home Secretary Charles Clarke of being "bitter" as the two clashed on BBC One's Politics Show.
Mr Clarke has made repeated calls for Gordon Brown to improve his performance or quit as prime minister.
Speaking from Labour's conference in Manchester, Mr Prescott said he wanted debate but Mr Clarke was just "bitter".
Mr Clarke hit back by saying he was only bitter about people who denied nothing was wrong with the party.
Mr Clarke fired his latest salvo against Mr Brown in an article for The Sunday Times.
He writes: "If Gordon Brown is to remain prime minister and prove wrong those who doubt his capacity to change, he must establish his authority and offer clear leadership.
"Confident communication, great speeches, a strong and supportive team and a coherent programme of policies flow only from a clear sense of political direction. There is no merit in just waiting for further dates or setting future tests.
"Although prevarication and evasion may appear attractive at the moment, they are actually the most dangerous course of all. The people we seek to serve will not be helped by a crippling lethargy or by just hoping that something will turn up."
Mr Prescott, who is leading calls for Labour MPs to unite behind Mr Brown, was tackled about Mr Clarke's remarks on the Politics Show.
He said: "I'm all for the argument. I've got no problem about that. The Labour Party always has arguments. It's had the Blairites and the Brownites. Now we've got the 'bitter-ites', quite frankly…."
Asked if he was saying Clarke was one of the 'bitterites', he replied: "Of course he's bitter. Charles knows that. I mean, Charles and I have been in the same room as Gordon and I've seen this kind of expression of bitterness. I'm sorry about that…".
Mr Clarke - who appeared wounded by the attack from a former cabinet colleague, said: "What I get bitter about is people who just listen and watch and get their heads down and say 'it'll be alright on the night'."
The former home secretary also called for the prime minister to stand down.
"I'm very sceptical personally about his capacity to pull it round and therefore I do think he probably should stand down. But I don't rule it out. He's a man of great quality, he was a very good Chancellor of the Exchequer and of course it's entirely possible he might, but I am - Jon - as you rightly say, a sceptic about his capacity to do that," he said.
John Prescott warned against party in-fighting during the party conference - and argued that a debate about the leadership could damage Labour's prospects.
"Be clear about it. You can't sign up for the fourth term and have six months rowing in the party. . Absolute nonsense."
Mr Clarke hit back by saying: "I'm not talking about six months. And John's quite wrong on his timings. The point is what John is suggesting is: don't discuss the question; walk into a wall."
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