Conservative deputy leader Michael Ancram has ruled himself out of the contest to replace Michael Howard.
Mr Ancram will return to the backbenches
He told the party's annual conference he had to be "realistic" that he could not "command the level of support" to make a successful leadership bid.
Mr Ancram, who is also shadow defence secretary, said he would return to the Tory backbenches after a new leader is announced in December.
There are five declared candidates in the contest.
Mr Ancram told party representatives in Blackpool he had "reflected long and hard" about running over the summer.
The former party chairman said any future leader would have his loyalty.
Mr Ancram ran for the job in 2001 but was eliminated in voting by MPs, prior to a wider poll of Conservative members.
The declared candidates for the current contest are: David Cameron, Ken Clarke, David Davis, Liam Fox and Sir Malcolm Rifkind.
The winner will be announced on 6 December.