The former Foreign Secretary threw his support behind his former cabinet colleague Ken Clarke as the politician who can "bring Gordon Brown down to size".
His departure will set off frenzied lobbying in the week before Tory MPs vote. The four remaining candidates will be battling to avoid coming last and being eliminated in the first ballot next Tuesday. A second ballot on Thursday week will decide the two whose names will go to a ballot of 300,000 party members.
Mr Rifkind's departure will mean a vital handful of extra votes for Ken Clarke, possibly enough to keep him in the final three.
Six other MPs had publicly pledged their support for Mr Rifkind, and his team claimed to have private pledges that brought his total to "between 10 and 20".
Asked how he expected his former supporters to vote, Sir Malcolm said: "I hope they'll support Ken, but I suppose that some will, and some will go elsewhere."
He added: "The Conservative Party must identify a credible and acceptable alternative Prime Minister and not just a new Leader of the Opposition as, otherwise, we will suffer the same fate as the Labour Party in 1992.
"Ken's combination of popular appeal and experience in office means he is best placed to lead us to victory." His announcement was a relief to the Clarke camp, which has faced increasing competition from the shadow Education Secretary, David Cameron. One of Sir Malcolm's prominent backers, Sir Patrick Cormack, also declared that he would support Mr Clarke.
Some of Mr Cameron's supporters had been hoping for Sir Malcolm's backing, although yesterday Ed Vaizey, a leading member of the Cameron camp, said: "I don't think we expected [him]to plump for David Cameron. He has known Ken Clarke for a long time and sat in Government with him for a very long time."
The shadow Foreign Secretary, Liam Fox, is in danger of being the first to be knocked out. He is battling with the front-runner, David Davis, for support from the right of the Tory party, while Mr Clarke and Mr Cameron are picking up support generally from the centre.
Mr Davis still appears to have a clear lead among Tory MPs, though not among Tories in the country. Sixty-five MPs have pledged to support him - nearly a third of the total
However, the Cornerstone Group of right-wing Tories have not yet decided whether to put up a candidate of their ownor back one of the declared candidates. If Mr Fox can secure their backing, he could push Mr Clarke into fourth place.
Sir Malcolm's campaign had a doomed look from the start, though he enjoyed a brief lift when his speech to the Conservative conference went down well, and he won an endorsement this week from the party's deputy leader and shadow Defence Secretary, Michael Ancram.
Later, Mr Ancram declared his support for Mr Cameron. He said in a statement: "I have decided to back David Cameron because I have come to the conclusion he is best placed to lead the Conservatives to victory at the next election."
Mr Cameron's team said that 29 MPs had now backed him publicly.Reuse content