Setting out his plans to make sure the London 2012 "Inspire a Generation" slogan is met, he said he wanted to end an "all must have prizes" culture and force pupils to think about beating their personal bests. The most recent Government survey of primary schools found more than 10,000 primary schools had fewer than half of their pupils competing against other schools three or more times a year and 1,950 had none at all.
A new draft PE curriculum, to be published in the autumn, will make it compulsory to take part in what Downing Street called "recognised and recognisable sports" such as football, hockey and netball. It will also prescribe "team outdoor and adventurous activity".
Mr Cameron said: "The idea of an Olympics legacy has been built into the DNA of London 2012 from the very beginning. Now the London Olympics has been a great success, we need to use the inspiration of the Games to get children playing sport more regularly.
"I want to use the example of competitive sport at the Olympics to lead a revival of competitive sport in primary schools. We need to end the 'all must have prizes' culture and get children playing and enjoying competitive sports from a young age, linking them up with sports clubs so they can pursue their dreams. That's why the new national curriculum in the autumn will include a requirement for primary schools to provide competitive sport."
Mr Cameron, who has said two hours per week is insufficient, has come under fire from teaching unions for suggesting the targets had led to a tick box mentality where some teachers did the minimum required.