Rear Admiral Chris Parry, who was appointed chief executive of the council two weeks ago, said the law was "very explicit" about how public benefit was defined and that schools were meeting the legal definition.
"It is not so much the new Charities Act that presents a threat to us, but its interpretation," he told MPs at a meeting of the Commons Select Committee on Children, Schools and Families.
"The definition of public benefit has not changed, only the interpretation placed on it by the Charity Commission. The definition of a charity fits every one of our schools at the moment. I am encouraging each of them to write to Dame Suzi Leather to show why they fit that particular charity status."
Andrew Hind, chief executive of the Charity Commission, told Third Sector he had not yet met with Parry, but intended to do so in the next few weeks.
Parry also said the Charities Act had produced "a flashpoint along the Berlin wall" and "heightened tensions" in the independent sector, because it had led schools to fear for their futures. He accused the commission of producing confusing guidance on fee-charging charities and public benefit.
"Part of the problem with the commission is that some of its guidelines are incredibly confusing," he said.
"In my experience, where there is confusion, there will always be nervousness and antagonism. The friction that is happening is not helpful to the debate."
Parry claimed that Charity Commission guidance did not appear to be in line with the law.
"It seems that the education mission, which justifies the charitable status of independent schools in the first place, has become of secondary importance to the social mission implied by some of the guidelines issued by the Charity Commission," he said. "Therein lies the threat."
2008: Chief executive, ISC
2005: Rear Admiral, Royal Navy
2004: Awarded CBE
2003-2005: Commander, UK Amphibious Task Group and NATO's UK/Netherlands
Amphibious Task Group
1994-1996: Commander, air defence destroyer HMS Gloucester
Education: Portsmouth Grammar School and Oxford University (Modern