Jeremy Corbyn must put the Labour party before his commitments to outside protest movements, Lord Prescott has said, nicknaming the leader's opponents "Bitterites".
The former deputy prime minister said there was a faction in the party that want to "continue the war" for control that they had lost.
But he warned that Mr Corbyn must find a balance between his job at the top of the party and his long-standing involvements in Stop the War Coalition, the Press Association reports.
It follows the leader's decision to ignore calls by senior figures to stay away from the group's Christmas fundraising dinner in the wake of a series of controversial statements it made about terrorism and air strikes on Syria.
Jeremy Corbyn arrives at the Stop The War Christmas fundraiser
Lord Prescott told Murnaghan on Sky News: "As the leader, he has earned the right democratically to lead the party.
"But there are some people in the party, who I call the Bitterites, who want to continue the war that they lost. The party has spoken, we have the leader and he has to recognise being a leader, perhaps, more than representing a protest movement.
"He's a different man, isn't he?"
He added: "At the end of the day Jeremy will have to decide there is a balance between what is the leadership of the Labour party and representing that, a very difficult job, and the one of having to carry out commitments (to) say, Stop the War.
"He's been in that all of those years. Do you just want him to say 'sorry, I'm not going to do it'? It's only a few MPs demanding that, by the way, not all the MPs.
"He's keeping to what he thinks are his principles and I have to say the electorate did seem to like to have a politician who still continues to do what he believed in.
"That's the difficult balance for Jeremy and he'll have to carry that out.
The peer said an "awful lot of people" supported the Labour leader and accused the media of being "obsessed" with Mr Corbyn.
"Let's get on with the job and give him a chance for goodness sake," he added.
Asked about reports that former London mayor Ken Livingstone could be given a peerage to bring him back into parliament, Lord Prescott replied: "Nothing's a surprise with Livingstone, is it? I mean I've been on the executive when I've had to vote for him and hold my nose because he didn't want to carry out the party's policy. That's Ken Livingstone."
Labour dismissed claims that Mr Livingstone was being lined up for a peerage.
A source said: "It's complete nonsense. There has been no discussion on peerages or names."
Appearing on the BBC's Sunday Politics programme, the shadow treasury minister Richard Burgon, said: "The attacks on Stop the War are proxy attacks on Jeremy Corbyn.
"We haven't had this previously.
"When Charles Kennedy was speaking at the 2003 demonstration against the Iraq War which two million people attended, the Liberal Democrats and Charles Kennedy weren't attacked for that and quite rightly so."