Supporters of Mr Cameron, 38, said they were appealing directly to David Willetts, Andrew Lansley, Alan Duncan, Sir Malcolm Rifkind, Tim Yeo and Liam Fox, to back their candidate.
"We are hoping that they will throw the towel in during the coming weeks and get behind David," said one leading member of his campaign team yesterday. "There will only be two candidates – the two Davids."
Pressure is growing on Kenneth Clarke to support Mr Cameron, after the latter made it clear he would not join a joint ticket with the former chancellor. That could leave the way open for a head-to-head contest between Mr Cameron and David Davis.
The Cameron camp said that Mr Davis would "hit a glass ceiling" in support. "David Cameron is building wider support whereas David Davis has been trying to get momentum by offering top jobs to would-be backers."
The Davis camp deny the claims, and remain confident their candidate is keeping a long lead. However, Mr Cameron appears to be building momentum. His campaign was joined yesterday by George Eustace, who resigned this week as head of the Tories' press office in a further signal that Mr Cameron has the tacit endorsement of Michael Howard.
In a speech which amounted to a personal manifesto, Mr Cameron, the shadow Education Secretary, said Tories had to refocus on issues such as doing more to encourage the family to stay together. Repudiating a Thatcherite legacy, he said: "We do think there's such a thing as society – we just don't think it's the same as the state."