Nominations for the Liberal Democrats leadership contest will open on Wednesday, in the hope of having a new leader in place before Parliament breaks up for summer, the party has revealed.
Greg Mulholland, the Lib Dem MP for Leeds North West, has protested the timetable, saying the party needs "strong leadership now".
Just eight Liberal Democrat MPs survived the general election, including outgoing leader Nick Clegg who announced his resignation on Friday.
However, the party's president Baroness Sal Brinton said they were prepared to "fight back", adding that more than 5,000 people had signed up since the results were announced, pushing membership above 50,000.
To get on the shortlist, contenders must secure the endorsement of 10 per cent of MPs - meaning currently just one person - along with 200 members from at least 20 local branches.
Tim Farron, one of the Liberal Democrats' last remaining MPs, has insisted that his party is not dead despite their dreadful showing in Thursday's General Election.
He told ITV News that if his party did not exist, "you would have to invent it".
He said: "We are absolutely going to fight back and rebuild from the grass roots, because the space is there that needs to be filled."
One of only eight surviving Liberal Democrats MPs, Greg Mulholland, has said the party's new leader must be someone who defied former Deputy Prime Minister Nick Clegg over student fees.
Mr Mulholland, who hung onto his seat in Leeds North West, has ruled himself out of the running but appeared to endorse Tim Farron with a call for a 'tuition fee rebel' to take over the position.
He said the controversy over the issue, along with backing NHS reforms and the so-called "bedroom tax" was one of "three fatal errors" made by Mr Clegg after he took the "right decision" to join forces with the Tories.
The 2010 failure to ensure no Liberal Democrat MP voted against a rise in fees was catastrophic. Now we need a leader who voted against.
Clearly those of us who have been re-elected will have to talk about how best we can work together and how we should operate going forwards over the next few years."
Business Secretary Vince Cable, Treasury Secretary Danny Alexander, former leader Charles Kennedy and Simon Hughes all fell, while at one point it looked like Nick Clegg himself would be toppled.
In all, it was a terrible night for the Liberal Democrats.
ITV News Political Correspondent Emily Morgan reports:
One of the Liberal Democrats' most high profile casualties of last night's election mauling has said voters who returned the Conservatives to majority power will only realise the impact of their decision in the coming days.
Simon Hughes told ITV News his party's core message is as "strong as ever" despite taking a "battering" at the ballot box.
The case for a fairer Britain and a fairer world hasn't gone away. In opposition we will rise to the challenge. We will take on the Tory government when we need to and I'm sure there'll be many many reasons for needing to take on the Tory government.
And I think many people will reflect over coming days that what we did in contributing to government made a huge difference for the better and that a Conservative majority government is now sadly not going to have that same fairness agenda, which we absolutely had as our central message.
Nick Clegg has stepped down from his position as leader of the Liberal Democrats following the party's devastating losses overnight.
In a stark resignation speech, Mr Clegg said "fear and grievance has won" after seeing his party lose scores of seats for what will be its worst ever election result.
Mr Clegg warned Britain's place in Europe and the world and future as a united kingdom "is now in grave jeopardy".
The former Deputy Prime Minister Nick Clegg is to make a statement about his position after election results that saw the Liberal Democrat representation in the House of Commons slashed.
Cabinet ministers Danny Alexander, Vince Cable and Ed Davey lost their seats in what looks likely to be the worst election result ever for the party.
This live broadcast has now finished.
Lord Ashdown has urged people to give Liberal Democrats leader Nick Clegg "space" to decide his future after the party suffered heavy losses in the General Election.
Lord Ashdown said Mr Clegg was "arguably the most decent man in politics" and added that he remained "proud" of the campaign run by the party.
Ed Davey, who lost his Kingston and Surbiton constituency to Conservative James Berry, has said he found "an awful lot of people wanted to vote for me but didn't want to vote for my party."
The economy was the most talked about issue on Facebook in the constituency that Chief Secretary to the Treasury Danny Alexander lost.
Over the course of the election campaign, the economy, environment, tax, health and Europe were the most discussed issues in the Inverness constituency.