Lord Mandelson has defended the prime minister
Business Secretary Lord Mandelson has urged Labour MPs not to sign a letter which calls on Gordon Brown to resign as prime minister.
Lord Mandelson acknowledged that MPs were in a "grumbly mood" but said forcing out the prime minister would not make things any easier for Labour.
The letter, addressed to Mr Brown and not widely circulated, says he could best serve the country by going.
It comes after Communities Secretary Hazel Blears quit the cabinet.
Lord Mandelson urged Labour MPs: "British politics is in a bad old state, nobody is happy and it's affecting all the parties.
"Don't please, through your actions, make it any worse for the Labour Party than for the other parties who have all got to come to grips with this crisis affecting British politics."
BBC Political Correspondent Reeta Chakrabarti said the business secretary was attempting to steady the ship but said his appeal may fall on deaf ears.
She said: "His words may not cut any ice with those who've drafted a letter to Gordon Brown asking him to go."
The BBC has seen a proposed letter to Gordon Brown from one Labour MP calling on the prime minister to resign.
It says Mr Brown has made "an enormous contribution" but adds: "We believe that in the current political situation you can best serve the Labour Party and the country by stepping down as party leader and prime minister."
The BBC understands Mr Brown's critics intend to send out some kind of "round robin" letter or e-mail to MPs, possibly on Friday, to test whether there is an appetite for a challenge to his leadership.
On Wednesday Health Secretary Alan Johnson was forced to deny he was ready to take over as party leader.
Mr Johnson told the BBC: "He is doing the job and there is absolutely no one who could do that job better."
Cabinet ministers Hilary Benn and Andy Burnham have also rallied round the prime minister and attempted to calm speculation he will be forced to quit.
Seventy Labour MPs would have to nominate a challenger to Mr Brown to force a leadership contest.
Attempts to gain enough support for someone to stand against Mr Brown for the Labour leadership have failed twice before - when he succeeded Tony Blair in 2007 and last summer.
The talk of a leadership challenge comes amid continued speculation about Mr Brown's planned reshuffle.
The BBC understands Mr Brown met John Reid on Tuesday, but the former home secretary is thought to have turned down the offer of a return to government, although No 10 sources say they talked mainly about football.
And a friend of Chancellor Alistair Darling has told the BBC that he would not accept any other job.
There are signs, too, that David Miliband may refuse to move from the Foreign Office.
Ms Blears had been tipped for the axe in the expected reshuffle. She had been under fire over her expenses claims despite repaying £13,000, following allegations she avoided paying capital gains tax on a property sale.
The Salford MP denied doing anything wrong but Mr Brown described her claims as "totally unacceptable".
She is said to believe she was being made a scapegoat by Mr Brown over the expenses issue.
Ms Blears's departure was the second top-level resignation this week, following Home Secretary Jacqui Smith's decision to step down, made public on Tuesday.
Ms Smith, who also faced expenses criticism, said she backed Mr Brown and denied Ms Blears was deliberately trying to undermine him.
In total, four ministers have said they will step down at the reshuffle. The other two are children's minister Beverley Hughes and Cabinet Office minister Tom Watson.