Mr Cameron said he hoped Education Secretary Michael Gove’s proposals for England would be “inculcated into the curriculum in any school in Britain”, BBC reported.
He was speaking amid concerns about an Islamist takeover in Birmingham schools – the so-called Trojan Horse claims.
Mr Gove said he wanted democracy, mutual respect and tolerance taught.
The government has asked Ofsted to introduce routine no-notice school inspections in England.
Speaking in Sweden after a mini-summit with other EU leaders, Mr Cameron said: “I would say freedom, tolerance, respect for the rule of law, belief in personal and social responsibility and respect for British institutions – those are the sorts of things that I would hope would be inculcated into the curriculum in any school in Britain whether it was a private school, state school, faith-based school, free school, academy or anything else.”
He added: “I think what Michael Gove has said is important and I think it will have the overwhelming support… of everyone in Britain including people that have come to settle in Britain and make their home in Britain.”