In a significant intervention, he indicated he would be in favour of the first new campus for a grammar school in 50 years, although the decision on this would be left to the education secretary, Nicky Morgan, to take in the next few weeks.
Michael Fallon, the defence secretary, is among those backing the proposal by the Weald of Kent grammar school in Tonbridge to open another campus in Sevenoaks.
Theresa May, the home secretary, has endorsed a similar proposal for a satellite grammar campus in her constituency of Maidenhead in Berkshire.
In opposition, Cameron warned his party to drop its obsession with grammar schools, saying it was a key test of whether the party was ready for power.
At the time, he said there would be no return to the 11-plus exam and more new grammar schools.
Michael Gove also vetoed the expansion of a grammar school to a new annexe while he was education secretary.
Questioned on the issue after a speech in East Sussex, Cameron said: “I strongly support the right of all good schools to expand. I think that’s very important and that should include grammar schools.
“Under this government, grammar schools have been able to expand and that is all to the good.
“I don’t want to pre-empt [Nicky Morgan’s] decision, that’s a decision for the education secretary to make. But the principle is very clear: good schools should have the freedom to expand.”
Senior Conservatives are said to want the expansion of the Kent grammar school to be approved before the election.
This article was written by Rowena Mason, political correspondent, for theguardian.com on Tuesday 17th February 2015 14.15 Europe/Londonguardian.co.uk © Guardian News and Media Limited 2010