Conservative members have reacted angrily to a policy speech last week which said building more grammar schools was the wrong way to boost children's educational prospects.
Cameron has promised to build more city academies, the privately sponsored state schools introduced by Prime Minister Tony Blair.
The issue has sparked a fierce debate within the Conservative party, which has traditionally supported private and selective education.
Cameron describes the row as pointless and sterile, noting that the Conservatives did not expand the grammar network during its 18 years of power before losing to Labour in 1997.
He told BBC radio he was not ''picking a fight'' over the issue.
''What I try to do is make sure that we have the right policy, right approach, that would achieve real aspiration, real social mobility, real opportunity for all children.
''And that is not having a ... rather pointless debate .. about grammar schools.
''It's about opening up the supply of more good school places, having firm policies on discipline, setting by ability so we stretch the brightest pupils.'' Since becoming leader at the end of 2005, Cameron has pushed the party away from the right with policies on the environment, health and social justice designed to appeal to the middle class voters who have kept Labour in power since 1997.
Cameron says building more city academy schools would do far more to improve the education of all children than expanding the few remaining grammars.
In an article on his party Web site he said the Conservatives would never be taken seriously by parents ''if we splash around in the shallow end of the educational debate, clinging on to outdated mantras that bear no relation to the reality of life today.'' ''It cannot be the limit of our ambition for some children to get a decent education: any party aspiring to government must aim to ensure a decent education for every single child.
''This is a key test for our party. Does it want to be a serious force for government and change, or does it want to be a right-wing debating society muttering about what might have been?'' REUTERS DS BD1503