Labour lost one of its safest seats in Glasgow East to the SNP
Senior Labour figures have been warning MPs not to plot against Prime Minister Gordon Brown, after the party's shock defeat at the Glasgow East by-election.
Ex-home secretary David Blunkett told backbenchers demanding a leadership contest to "grow up".
Justice Secretary Jack Straw had been touted as a caretaker leader, but he has made it known he wants Labour to close ranks behind Mr Brown.
However, he is yet to come out publicly in support of the prime minister.
The BBC's Nick Robinson says Mr Straw is said to be urging rebels to calm down, but has not come out with a "full-throated" declaration of approval either.
Several MPs are reported to have urged Mr Straw to lead a challenge to Mr Brown's leadership in the autumn unless the party's fortunes improve.
Cabinet Office Minister Ed Miliband has dismissed reports that colleagues wanted Mr Brown to stand aside.
He told the BBC's Newsnight: "I do not recognise those comments from the Cabinet colleagues I talk to."
He urged Labour MPs to keep faith with the prime minister, who he called the "right man" to take Britain through the current economic downturn.
Labour is holding its National Policy Forum at Warwick University, where ministers, unions and activists are thrashing out a blueprint for the next election manifesto.
The BBC's Iain Watson is at the forum and he said informal discussions were going on about the prime minister's future.
John Hannett, general secretary of the UK's fourth biggest union Usdaw, is attending the meeting and he told the BBC it would be about "policy, not conspiracy theories".
While he admitted Labour had fallen on its hardest times for years, he said it was about "holding our nerve and debating the real issues".
GMB union leader Paul Kenny said Labour backbenchers should "get on with it" if they wanted Mr Brown out.
Mr Kenny said: "Most of the speculation and tittle-tattle has been about when he's going to go, who's going to do him in, what's the next big landmark event that will force him to resign.
"The MPs have got to have the courage of their convictions if they've got them, and my advice to them is 'get on with it'."
Former home secretary David Blunkett told BBC Radio 4's Today programme that unlike the Conservatives, Labour was not a "hatchet job" party which would ditch a leader at the "drop of a hat".
Reports suggest Jack Straw is being urged to lead a revolt
"If people are concerned about food and fuel prices and what's happening with the world economy, changing the leader changes nothing," he said.
He urged Labour MPs to get back into the neighbourhoods they represent and rebuild the party's fortunes.
Mohammad Sarwar, Labour MP for Glasgow Central, said he was 100% behind the prime minister, and blamed the world economy for the government's unpopularity.
Former transport minister Dr Stephen Ladyman said he believed there was no appetite for a leadership contest.
"There will be one or two individuals calling for that, of course there will," he said. "But I don't think there's any stomach for that."
He urged the prime minister to "come out fighting".
The SNP won Glasgow East - previously considered one of Labour's safest seats - by 365 votes, achieving a 22.54% swing.
Conservative leader David Cameron has demanded that the prime minister call a general election after he returns from his summer holiday.
Meanwhile, the prime minister received reassurance from US presidential candidate Barack Obama, who is visiting the UK as part of his overseas tour.
Speaking outside No 10 after two hours of talks, Senator Obama said: "You're always more popular before you're actually in charge.
"Once you're responsible then you're going to make some people unhappy."