Shadow health secretary Andrew Lansley has ruled himself out of entering the Conservative leadership race.
Mr Lansley is shadow health secretary
The Cambridgeshire South MP previously said he would stand if he could win.
"Having talked with colleagues I have come to the conclusion I don't have enough support, therefore I shall not be standing," he told reporters.
Mr Lansley said he expected Ken Clarke and David Davis to battle out the final round of the contest, but he had yet to decide who to support.
He added: "I welcome the debate about the future of the party and the fact that everybody now accepts that we have to change, particularly to win back voters in their 20s, 30s and 40s."