Labour and the Conservatives have clashed on the issue of trans rights, as Sir Keir Starmer said it was wrong to say “only women have a cervix” and the health secretary, Sajid Javid, said this was a “total denial of scientific fact”.

The Labour leader called for laws to go further to protect trans rights after he was asked about one of his MPs, Rosie Duffield, who said “only women have a cervix”.

She is not attending the party conference in Brighton after receiving threats and being called transphobic.

Starmer called for a “mature and respectful debate” about trans rights, as he warned that trans individuals are among the “most marginalised and abused communities”.

He declined to call her remarks transphobic but asked about them on The Andrew Marr Show on BBC One, he said: “It is something that shouldn’t be said. It is not right.

“I spoke to Rosie earlier this week and told her conference is a safe place for her to come.

“We do everybody a disservice when we reduce what is a really important issue to these exchanges on particular things that are said.”

In response, Javid accused Starmer of a “total denial of scientific facts”, adding: “And he wants to run the NHS”.

He drew criticism from trans rights activists and allies, with many pointing out the NHS advice that trans and non-binary people with cervixes should make sure they get smear tests. Trans men registered with their GPs as female automatically get invited, while trans men registered with their GPs as male have to ask for smear tests.

Trans Actual, an organisation campaigning on trans issues, said it was “disgusted to see [the health secretary] denying the reality of trans men and non-binary people].”

It added: “Lots of us have cervixes. Lots of us would like them removed actually.”

Some Tory MPs weighed in behind Javid’s position. Jackie Doyle-Price, a Tory MP and former minister, said: “But it is right Keir. Only women have a cervix.”