Ex-prime minister Sir John Major has urged Tory right-wingers to back David Cameron, saying he is the party's best chance of winning the next election.
Sir John Major was Conservative leader from 1990 to 1997
Mr Cameron should not "go out of his way to seek a fight" with the Tory right, but neither should he water down his beliefs to appease them, he said.
Setting out attractive, long-term policies was the way forward, he said.
He spoke out after ex-Tory chairman Lord Tebbit dismissed Mr Cameron's modernising talk as "clever marketing".
Sir John said he wanted "those people who nibble away at the party" to back their new leader to make the party electable again.
He told BBC News 24's Hardtalk programme: "David Cameron shouldn't go out of his way to seek a fight with the right wing, but neither should he move away from the policies that he thinks, and I believe, will actually make the Conservative Party an attractive electoral force again.
"If some disagree, so be it. They will have to disagree - that's in the nature of politics."
But he insisted: "We have moved on."
He said the chance of Mr Cameron winning the next election, expected in 2009, when Labour will have been in government 12 years, was "far better than most people realise".
But this depended on the party being able to "set out a credible selection of long-term policies that people will find attractive and provided those people who nibble away at the party decide to give it their support, rather than their grudging opposition".
Sir John defended claims by critics that Mr Cameron's attempts to change the party had so far not produced any firm policy proposals.
He said the leader had about 12 to 18 months before he needed to make any such pronouncements.
"Of course they won't all come out on the same day," he said. "I mean there will be other policy groups that will report in advance of that, so there will be general accretion of policy ... as we move forward."
Turning to Iraq, Sir John said he did not think it was likely that British troops would withdraw from the region in the near future.
"I think there will come a time, some time in the next five or six years, when the Iraqis will say: 'We no longer wish you to be here'," he said.