The 39-year-old shadow Education Secretary, whose performance at last week's Tory conference has taken him from outsider to bookmakers' favourite, dismissed as "just rubbish" the idea that he was "Tory Blair".
He told BBC Television's Sunday AM programme: "I think there are two sorts of politicians in this world, there are those who come into politics to tell people what to do, that's Tony Blair. And there are those who come into politics to set people free. That is David Cameron and the Conservative Party."
He continued: "People don't want a party that's trying to turn the clock back to 1997. They want us to understand what's changed and to be relevant today, for the challenges we're going to have after Blair, because he's going. We're going to be facing Gordon Brown. And I think all elections come down to a simple question - who's the party of the future, who's the party of the past?
"There is no Clause IV, there is no magic wand, there is no one single thing that the party has to do."
Mr Cameron again refused to confirm or deny he had smoked cannabis. "I did lots of things before I came into politics that I shouldn't have done. We all did," he said. "I didn't know I was going to be a politician."
With Tory MPs holding their first leadership ballot a week tomorrow, Mr Cameron's pitch is that he can revive his party's fortunes in the way Mr Blair transformed Labour without being dismissed as "all image, no substance".
David Davis, the early frontrunner who lost momentum last week, took a sideswipe at his younger challenger by saying he would not replicate Mr Blair's image-driven approach. He told the BBC's Politics Show: "I recoil against that. I'm afraid that's me. At the end of the day, if the Tory party say, 'We need a charlatan', they are not going to pick me."
But Mr Davis showed a softer side when he became emotional about his constituents in Howden and Haltemprice. "There is a love affair with them, I care about them, and that's what drives me and that's what drives my relationship with them," he said.
Liam Fox, who is trying to woo right-wing MPs from Mr Davis, warned Tories to be wary of choosing a leader on the basis of image. He said: "I think there's been a little too much of this cult of personality recently in our politics, because the Yory Party will ultimately be judged by the electorate not by how we look or the age of our members but on what we intend to bring to our country." Lord Heseltine, the former deputy prime minister, urged Mr Cameron to "learn the trade" by serving under Kenneth Clarke before taking over as leader when he had more experience.
Mr Clarke could take some comfort from a BBC survey showing he remains the favourite choice of the public at large, on 27 per cent, with Mr Cameron and Mr Davis on 13 per cent. A YouGov survey of 746 Tory members put Mr Cameron on 39 per cent, with 26 per cent for Mr Clarke and 14 per cent Mr Davis.