Dominic Raab said he would “probably not” describe himself as a feminist but insisted he was committed to equality.
The former Brexit secretary was challenged over a 2011 comment that some feminists are “obnoxious bigots”.
The Tory leadership contender said: “The point I was making is that sexism is wrong and it’s wrong if it’s said about a woman or about a man and I think equality is too precious a value for us to put up with double standards.
“I do think we should call hypocrisy out in political debate and political life.”
Asked on ITV News whether he would describe himself as a feminist he said: “No, probably not.
“But I would describe myself as someone who’s a champion of equality and meritocracy.”
Referring to his wife, Erika, he said they were a “two salary couple, I support her as much as she supports me”.
“I’m all for working women making the very best of their potential and that’s something that’s really important to me.”
Mr Raab, a prominent Brexiteer, played down the prospect of Speaker John Bercow helping to block a no-deal departure from the EU.
“I don’t think that will affect the chances and I think Parliament should of course have its say right the way through this.
“But actually I think it’s very difficult for Parliament to frustrate Brexit if the Government is serious about keeping our promises to the people of this country.”
He insisted that a no-deal Brexit was not his preferred option and said he would use “every ounce of energy” to work for a better offer from the EU.
“But if they don’t move we must give this country a sense of direction, get out of this rut and take Britain forward and that’s what I’d do.”