Michael Howard has been urged to stay on as Conservative Party leader to ensure a smooth succession.
Mr Howard said he was stepping down as he had failed to deliver the win he had promised. The party won 197 seats, up 33 on 2001, failing to oust Labour.
He has already said he planned remain in post until the Tories had reviewed their leadership election procedures.
But Tory former deputy prime minister Michael Heseltine urged him to stay for the referendum on the EU constitution.
Measures brought in by William Hague gave the final say on leadership to party members rather than MPs.
Some Conservatives believe it was a mistake to hand this power to the grassroots membership as they tended to be older and to have little understanding of what was required of a leader.
Lord Heseltine said the parliamentary party must be allowed to decide who led the party .
"They are the ones who can balance the views of the party and the political reality of winning power," he said.
Any new leader must "enthuse activists" and be able to win over voters in the "middle area", he added.
"The party has to be given the time to see the performers in action and to gauge the public reaction to them."
'Mountain to climb'
But Mr Heseltine also argued that Mr Howard should stay on to fight any referendum on the EU constitution - which he said could be very divisive for the party.
A referendum is not expected until some time in 2006.
"If we get that behind us, get a proper period to look at the candidates for leadership, get the rules changed then I think the Tory party can be in a position to win 140 (extra) seats in one election.
"But there is a mountain to climb."
Shadow minister for deregulation John Redwood said it was important any reforms avoided losing "all contact with the membership". He also refused to rule himself out of the leadership race.
Other likely candidates include Shadow Home Secretary David Davis, Shadow Chief Secretary to the Treasury George Osborne and policy chief David Cameron.
Shadow Chancellor Oliver Letwin was quick to rule himself out of the running.
But co-party chairman Liam Fox said it was "too early" to say whether he would stand for the job.
He added that the party needed to have a "long look at what happened in the campaign" and to think about how it would position itself in the new Parliament.
The party had been "more efficient and disciplined" on the ground, but that needed to be built on, he said.
The shadow cabinet line-up would remain same despite the party's election defeat, he added.
Former Tory minister Stephen Dorrell called for the party to engage in some self-examination in a bid to win wider support.
"It's regrettable that we are going straight into this discussion of personalities before we have a discussion about where we want to be."
Shadow International Development Secretary Alan Duncan said the Tories had failed to "reconnect" with a new generation of voters.
The party had done a "good job in shoring" its traditional support, but if it was break through in this "ever-more difficult three-cornered contest" then the Tories had to start thinking, he said.