Tom Harris told the meeting Gordon Brown could not win the next election
A Glasgow MP has become the first Scottish Labour MP to suggest Gordon Brown stands down as prime minister.
Glasgow South MP Tom Harris said he did not think Mr Brown should lead the party into the next general election.
Speaking at a Parliamentary Labour Party meeting, Mr Harris added that he felt compelled to express his views.
The group's chairman, Tony Lloyd, said he was convinced there was no serious threat to Gordon Brown's leadership after he was backed by most MPs.
Writing on his blog, Mr Harris said he told the meeting: "If there's one thing that unites this PLP, it's a determination to win the next election.
"And those of us who have come to the conclusion, by an entirely objective and logical process, that you cannot lead Labour to victory, would be doing a disservice to our country and to our party by staying silent."
In the wake of Labour's European election result, which saw the party at UK level beaten into third place by UKIP, Mr Harris wrote: "The results from last night have confirmed in my mind that the electorate aren't yet sold on Cameron, but they have made their minds up about you, Gordon, and it's not going to change.
"We can win the next election, but only if we have a new leader."
Mr Harris added: "So answer me this, Gordon: Why do you think Cameron wants you to remain in post?"
Scottish Secretary Jim Murphy said Mr Harris was wrong.
He told BBC Scotland: "Tom Harris and I are neighbouring MPs and we are good friends. He's entitled to his view but he is wrong."
He said the prime minister was "uniquely qualified" to deal with the "enormous challenges of the economy and so much else".
Labour MP for Paisley and Renfrewshire North, Jim Sheridan, said it was mainly former ministers who were upset at their treatment by the prime minister who were behind any rebellion.
Mr Sheridan said: "The Labour Party is bigger than these people. We have to move on.
"Either they move on with us or they move out. It is as simple as that. We can't tolerate this kind of behaviour any longer."
Ian Davidson, MP for Glasgow South West, said there was no credible alternative to Mr Brown's leadership.
He said: "It was quite clear from the debate and the way the responses were going in the meeting that people thought that Gordon and his policies were the right ones to take us forward.
"It was very noticeable that there was very little that divided the protagonists on policy issues, so this was simply a question of personality.
"I think that undercut the approach that those who wanted another election had."