Conservative frontbencher David Willetts has ruled himself out of the Tory leadership race and thrown his support behind David Davis.
Willetts has dropped out of the leadership race
The shadow trade secretary said Mr Davis had the experience and authority.
Mr Willetts, nicknamed "Two Brains", is on the modernising wing of the party and backed Michael Portillo's campaign in the 2001 leadership election.
But one of Mr Willett's backers, Charles Hendry, has now declared his support for Ken Clarke.
Mr Willetts has outlined his ideas on the party in a series of speeches and articles.
The Havant MP says the Conservatives need to focus as much on social justice and building a strong society as they do on the economy.
On Thursday Mr Willetts said those ideas had received widespread support but he would not be a candidate.
In a statement he praised Mr Davis, saying: "He has demonstrated that he has the support of many senior figures representing different strands of opinion within the party.
"He is widely respected and he has the credibility to unite the Conservative Party once the leadership election is over.
"He recognises the scale of the task ahead of us and he has the energy and determination to lead us to victory.
"As we have seen in recent months he has the empathy, understanding and gravitas to address the challenges facing Britain and the wider world."
A source from supporters of David Cameron, another Tory moderniser, shrugged off the news.
He said: "It is more of a blow to Ken Clarke - there had been an expectation that David Willetts might well back him. Ken Clarke is not making any progress at all in terms of gaining support of the new intake or the modern Conservative Party."
Sir Malcolm Rifkind
The source said Mr Cameron's campaign was confident of picking up support from some of the four MPs who had been publicly backing Mr Willetts.
But one of those backers, Tory vice-chairman Mr Hendry, said Mr Clarke was best placed to lead the modernising agenda and put the Conservatives back into government.
Mr Hendry said: "He can win over young people who have never voted Conservative in past elections, first-time voters, and those whose values are instinctively Conservative but who have drifted to Labour and the Liberal Democrats."
Mr Clarke continued his pitch for the leadership on Thursday with a withering attack on Tony Blair's "autocratic" style of government.
Former foreign secretary Sir Malcolm Rifkind used a speech to argue it was time to reassert the One Nation strand of Conservatism and bring it up to date.
Sir Malcolm said the Tories since 1997 had spent too much time trying to reflect the nation's fears instead of advancing people's hopes.