Gordon Brown's decision to stand down as Labour leader was swiftly welcomed by Labour MPs.
John Mann, who became the first Labour backbencher to call for him to go on Saturday, hailed it as a "wise and brave" decision.
He said the party now needed to "regroup" to fight the Tories in Opposition.
Slough MP Fiona Mactaggart, who has criticised Mr Brown's leadership in the past, said he had done the "right thing".
"It is a recognition that Labour lost the election, which I think has not been made clear until this point," she told BBC Radio 4's PM programme.
"I understand that the constitutional position is that he remains Prime Minister and that's an issue so he needed to stay on in that role.
"I don't know why it took him until today to say that he felt that there should be a new future leader of the Labour Party. It's a hard decision to make."
There were a "number of really well-qualified candidates" who could replace Mr Brown, Ms Mactaggart added.
Mr Mann (Bassetlaw) said it was better for Mr Brown to secure his place as a successful Chancellor rather than "hanging on".
On Sky News, he denied there would be any "rejoicing" in the party.
"We've just lost the election. We've a minority Tory government that wants to make public sector cuts that we need to fight against.
"That's why we needed a new leader to regroup and take on this Tory onslaught on our public services.
"It is the right decision. It allows us to move forward. But we've just lost an election. We need to get real."
Sir Stuart Bell (Middlesbrough) said Mr Brown had offered a "viable alternative" to the Tory party.
Labour and the Liberal Democrats were closer on the economy and would avoid the kind of cuts the Tories were threatening.
"Gordon has been very wise, very sensible and very courageous."
SNP Westminster leader Angus Robertson MP commented: "After Thursday's result, it was inevitable that Gordon Brown would have to stand down. He has done the right thing.
"From the outset of these negotiations, the SNP have made it clear that we believe a progressive alliance can deliver the best result for the people of Scotland - rather than a Tory government which was resoundingly rejected by the people of Scotland last week, with the Tories in fourth place north of the Border.
"We welcome the news that Labour and the Liberal Democrats are now moving towards this.
"The SNP stands ready to work with other parties in an arrangement which will deliver a functioning parliament at Westminster."
Former Labour MP Ann Keen, who served as Mr Brown's parliamentary aide for seven years but lost her seat at the election, told BBC Radio 4's PM programme: "It is a very sad day for the values we all hold very dear, because Gordon Brown is the most obvious man to lead not only the Labour Party but to lead this country.
"But considering how the people have voted, I understand what he has said. But the reality is that we have lost a great Prime Minister and a great man on the world stage."
Mr Brown's close Commons ally Geoffrey Robinson told PM: "The step the Prime Minister has taken, and the Liberals and Labour Party are trying to work out between themselves now, is by far the best way forward.
"It is sad for him, of course. It is sad for many of us who know him. But he is not one to dwell on it. He will bounce back. He will be strong in this situation.
"What he has done, I believe, is in the national interest."
Labour's former London mayor Ken Livingstone said: "I think it is good that he has made it clear he is not going to put his own career and ambitions ahead of what is best for the country and the Labour Party.
"I'm not at all surprised that it's been difficult for the Lib Dems to get agreement with the Tories. It's much easier to put together a package between Labour and the Lib Dems."
Mr Livingstone said that the succession contest would offer "a clear choice between left and right - David Miliband will be the candidate of the right and we are not yet clear whether it will be Ed Balls or Ed Miliband as the candidate of the left".
Plaid Cymru MP Elfyn Llwyd said: "Gordon Brown has done the decent thing following the overwhelming rejection of his premiership last Thursday. It was clear that he had no mandate from the people to maintain his position in Downing Street, and he has now shown that he has heard that message loud and clear.
"Mr Brown's announcement is a signal to other progressive parties that Labour is willing to talk in order to explore the possibility of establishing a progressive alliance to govern in Westminster."
Welsh Labour leader and Wales's First Minister Carwyn Jones said: "There have clearly been significant problems with the negotiations that have taken place between the Tories and Liberal Democrats, in arriving at an agreement.
"Nick Clegg has now instead, requested formal negotiations with the Labour Party, with a view to exploring an alternative way forward and this is patently an important development.
"The Labour Party will engage with utmost sincerity and determination at these negotiations, to seek a successful outcome.
"The fact that Gordon Brown is selflessly putting the interests of the country first at this crucial juncture, speaks volumes about the man - as both the leader of our country and our party. For this he can only be admired.
"It will be crucial that any new government protects Wales from the brunt of excessive spending cuts."
Labour's former environment minister Michael Meacher, who unsuccessfully attempted to mount a bid for the leadership when Tony Blair resigned in 2007, said: "It is the right decision to stand down to pave the way for the renewal of Labour, which is now so urgently needed.
"The election result was not a judgment on a single individual but rather on the collective failure of New Labour over bank reform, privatisation of public services and the ballooning of inequality which shames our society.
"A social partnership economy is now needed which embraces the working class as well as middle England and a new Labour leader is needed who can deliver that."
Mr Meacher said he would not be putting himself forward as a candidate to replace Mr Brown.