Former Foreign Secretary Sir Malcolm Rifkind has pulled out of the race to be the next Conservative Party leader.
Sir Malcolm is now backing ex-Cabinet colleague Ken Clarke.
The 59-year-old had been supported publicly by six other MPs. One of them, deputy Tory leader Michael Ancram, says he is switching to back David Cameron.
Meanwhile, the Cornerstone Group of right-wing MPs has decided it will not field a candidate. Edward Leigh had suggested he could represent the group.
After a meeting on Tuesday night, the group said it would decide whether to recommend one of the existing candidates after seeing them in action at a hustings on Wednesday.
But one of the group's leading MPs, John Hayes, has declared his support for shadow foreign secretary Liam Fox.
There are now four known leadership contenders: Mr Clarke, Mr Cameron, Dr Fox and David Davis.
Sir Malcolm, a rank outsider in the race, told BBC News he had won far less support than he would have liked.
"There is no realistic prospect of me coming through," said the 59-year-old shadow work and pensions secretary.
His departure means that by Thursday next week MPs should have whittled down the choice of candidates to the two who will go to a ballot of all Tory members.
Sir Malcolm said Mr Clarke was "head and shoulders" above the rest as a potential prime minister.
He warned: "If we try to choose a leader of the Opposition, that is what we will end up with, someone like Neil Kinnock in 1992 will not be able to get the public support that is required.
"So I think Ken Clarke has the popular appeal, he has the experience, he is an obvious person who can handle Gordon Brown, who will be prime minister by the time of the next election, and that has influenced my judgment."
The Kensington and Chelsea MP said he could not deliver a "bloc" of supporters to Mr Clarke's campaign - his backers would make up their own minds.
Wednesday: Hustings in front of right-wing Tory MPs from the 92 Group, No Turning Back Group and Cornerstone Group
Thursday: Nominations close. Hustings for the Contact group of Tory spouses
Monday: Possible hustings for all Tory MPs
Tuesday: First round of voting by MPs
Early November: Tory members start voting on final two candidates
6 December: Result expected
The Cameron campaign says it never expected to win over Sir Malcolm but is celebrating the prize of Mr Ancram's support.
The deputy party leader said Mr Cameron brought "a fresh dimension to Conservative politics".
Earlier, Mr Davis admitted in a Daily Telegraph article that "flamboyant platform oratory" was not his style but argued it was "substance" which counted.
His ally Damian Green said the campaign was "back on track" after criticisms of Mr Davis' Tory conference speech.
The pace of the campaign is hotting up ahead of the first round of voting on 18 October.
All the candidates will appear before around 80 right-wing MPs at a hustings for the members of the 92 Group, the No Turning Back Group and the Cornerstone Group.
And the contenders will get their chance to woo the female Conservative vote when they are questioned by the Contact Group of Tory spouses on Thursday.
The first round of voting by Conservative MPs is next Tuesday, with the candidate receiving the fewest votes being eliminated.
That process is then repeated two days later.
The estimated 300,000 Conservative members nationwide then have the final say. A result is due on 6 December.