Dominic Raab has rejected the idea that misogyny should become a hate crime in the wake of the Sarah Everard murder, but then appeared confused about its meaning as he suggested it could apply to abuse against either women or men.

The justice secretary, who has said he is not a feminist and previously complained about the “raw deal” men are getting, said it was his “number one priority to make sure women feel confident in the justice system”.

However, pressed on BBC Breakfast about whether misogyny should be a hate crime, he appeared not to understand the term as he said “misogyny is absolutely wrong, whether it’s a man against a woman or a woman against a man”.

Misogyny is hatred aimed specifically against women, and some campaigners would like to see it criminalised.

Questioned about his confusion, Raab said: “What I meant was, if we are talking about things below the level of public order offences of harassment, intimidation, which are rightly criminalised – if we are talking about, effectively, insults with a sexist basis, I don’t think that criminalising those sorts of things will deal with the problem that we have got at the heart of the Sarah Everard case.”

He said the problem was with enforcement, rather than a lack of laws, supporting Boris Johnson’s views that a hate crime of misogyny was not necessary.

Raab also downplayed statistics that show less than 1.4% of alleged rapes are prosecuted, saying most crime data is examined at the point of charge.

“The conviction rate statistics are often, I’m afraid, rather skewed,” he said. “If you look at the normal way that people measure the conviction rate – as a proportion of the number of prosecutions that are launched – actually once you get to court, there is more or less around a 70% chance of conviction.

“The challenge we’ve got is the reporting of cases … through to the preparation of the file that goes to the CPS and then the decision to prosecute… the critical thing is getting the cases to trial with the evidence to secure that conviction.”

Asked about accusations that misogynistic attitudes are tolerated in policing, Raab said it was precisely why the government had ordered an inquiry into the circumstances of Sarah Everard’s murder by a serving police officer. He said some systemic changes would need to be put in place.

“I know many, many incredibly dedicated police officers, men and women, who are appalled by this and are determined to fix this problem. But we do need to look at culture in the police and the second phase of the review, the inquiry the home secretary announced, is target at that issue,” he said.

Speaking later on BBC Radio 4’s Today programme, Raab acknowledged that the long backlog of cases in the courts was due partly to cuts in the criminal justice system, adding that he hoped it could be cleared within six to 12 months.