Lord Adonis, the schools minister, told the annual meeting of the Headmasters' and Headmistresses' Conference that the state sector needed their "educational DNA" to improve standards.
He placed pressure on the fee-charging headteachers by claiming that 800 state secondaries, around one quarter of the total, were failing to provide a good enough education, with fewer than 30 per cent of pupils achieving five good GCSEs including English and maths. The support of private schools would give all children access to an excellent education, not just those that could afford expensive fees, he said.
But Bernard Trafford, the chairman of the HMC, warned the Government to keep its "hands off" the independent sector. Dr Trafford said creeping government regulation was putting their independence under threat. He also accused ministers of trying to "nick" the word independent by claiming academies were independent when they had to teach core elements of the national curriculum, had no freedom over admissions and were inspected by Ofsted.
Lord Adonis was at the HMC, which represents 250 of the country's most academically focused fee-charging schools, to launch a new academies and independent schools prospectus. It says the programme offers a "once-in-a generation opportunity" to bring independent and state schools together and confirms that independents, in line with universities, will not have to pay pound;2 million as sponsors.
The National Union of Teachers published its own report on academies this week, which details their opposition to the programme, including the impact on pay and conditions and admissions policies.
Steve Sinnott, the union's general secretary, described the wooing of private schools to sponsor academies as "extraordinary". "I reject the implication that private schools and the quality of teaching within them are better than in state schools," he said. "Teachers in socially deprived areas make an enormous contribution to the lives of their pupils."
More than 20 independent schools, including Wellington College and Dulwich College, are now involved in 47 academy projects.
Birkenhead High School, a private girls' school, announced its intention to switch to the state sector by becoming an academy. And Woodard Schools, a private schools education trust, said it plans to sponsor three academies in West Sussex in partnership with the local county council.
However, it was revealed the Government had turned down approaches from other private schools. Lord Adonis said only high-performers in areas that needed academies would be considered.
The Forum of Independent Day Schools, representing 65 schools which include some of the largest and most academically successful in the country, said the Government failed to talk properly to the sector.
"We dispute the suggestion that sponsoring academies or becoming academies ourselves are the only ways we can promote social mobility," a spokesman said.
Chris Ray, high master of Manchester Grammar School, said: "Our expertise is dealing with very able children so there may be some schools in HMC that can help pupils of all abilities but we cannot."
Lord Adonis refused to be drawn on the question of charitable status and whether backing academies would have an impact. New rules mean that independents will have to offer places to children from poorer backgrounds in order to maintain tax breaks worth around pound;100 million a year.