Rishi Sunak should apologise as “swiftly as possible” for his transgender joke, Sir Keir Starmer has said, as the Prime Minister resists a call from Brianna Ghey’s father to express regret about the remark.

The Labour leader said the PM should “do the right thing” after Peter Spooner, Brianna’s father, demanded he say sorry for the “dehumanising” and “degrading” jibe.

Mr Sunak had accused Sir Keir of being incapable of “defining a woman” in an attack on Labour U-turns in the Commons while Esther Ghey, Brianna’s mother, visited Parliament.

His comment prompted fierce criticism from across the political spectrum, with Sir Keir telling Mr Sunak: “Of all the weeks to say that, when Brianna’s mother is in this chamber. Shame.”

Speaking to reporters on Thursday, the Labour leader said: “This is nothing to do with me. This is Brianna’s father. They’ve had their child murdered and he has put his words out about what the Prime Minister said and it’s not good enough for the Prime Minister’s team to go out today and effectively say to Brianna’s father ‘you didn’t understand what Rishi was saying’.

“He did understand. He’s given his reaction. The right thing to do is to apologise as swiftly as possible – not just reflect but apologise. This is a grieving father.”

Cabinet ministers have defended the Prime Minister over the remarks, insisting they were not directly connected to Brianna’s case, with Kemi Badenoch accusing Labour of trying to “weaponise” the exchange in its criticism.

Asked about the Business Secretary’s claim, Sir Keir said: “She’s completely and utterly wrong. The idea that I’m responsible for Rishi Sunak’s comments is through the looking glass.”

Mr Sunak’s remarks have drawn criticism including from within his party ranks, but he declined to honour Mr Spooner’s call for an apology on Thursday.

On a visit to Cornwall he told reporters: “Like everyone, I was completely shocked by Brianna’s case. To have your child taken from you in such awful circumstances is almost impossible to come to terms with, and for Brianna’s mum to talk with such empathy and compassion about that, I thought, was inspiring, and it showed the very best of humanity.

“I’ve nothing but the most heartfelt sympathy for her entire family and friends.

“But to use that tragedy to detract from the very separate and clear point I was making about Keir Starmer’s proven track record of multiple U-turns on major policies, because he doesn’t have a plan, I think is both sad and wrong, and it demonstrates the worst of politics.”

Asked to respond to Mr Spooner’s demand for an apology, Mr Sunak insisted his comments had been “absolutely legitimate”.

“If you look at what I said, I was very clear, talking about Keir Starmer’s proven track record of U-turns on major policies because he doesn’t have a plan,” he said.

Ms Ghey, on the Facebook page of the Peace & Mind UK campaign she set up in her daughter’s memory, later wrote: “I don’t wish to comment on reports of wording or comments recently made. My focus is on creating a positive change and a lasting legacy for Brianna.

“Through Peace & Mind, we want to improve lives by empowering people, giving them the tools they need to build mental resilience, empathy and self-compassion through mindfulness. In developing these skills, I hope that we can create a more understanding, peaceful and stronger society for everyone.”

Cabinet minister Penny Mordaunt suggested Mr Sunak had “reflected on things” after his comments.

The Commons Leader said: “Whatever the rough and tumble of this place, whatever the pressures and mistakes that are made in the heat of political combat, we owe it to the people who sent us here to strive every day to make them proud of us and this place.”

She added: “That is not just about (Brianna’s parents) that he should reflect on, but I am sure he is also reflecting about people who are trans, or who have trans loved ones and family, some of whom sit on these green benches.

“I hope the leader of the Opposition will also reflect on his actions too.”

Tory former business minister Paul Scully told the BBC’s Politics Live: “If it was me, I would probably pick up the phone to Brianna’s father, frankly.”

Earlier, policing minister Chris Philp said Mr Sunak is “very keen” to meet Brianna’s family and it is understood Number 10 has reached out to arrange a meeting.

Brianna’s mother had been in Westminster during PMQs with her local MP in Warrington, Charlotte Nichols, as she campaigns for mindfulness lessons to be taught in schools following the killing of her daughter.

Brianna was stabbed to death by teenagers Scarlett Jenkinson and Eddie Ratcliffe in a Cheshire park last February.

During their sentencing earlier this month, the judge said the “exceptionally brutal” murder had elements of both sadism on the part of Jenkinson and transphobic hate on the part of Ratcliffe.

Downing Street rejected the suggestion that Mr Sunak repeatedly used transgender people as a punchline or a joke, but made clear his views on gender identity have not changed.

“He’s said that it shouldn’t be controversial to be clear on what the definition of a woman is. That’s not least because of the fundamental facts of biological sex being critically important in areas such as healthcare and other services,” his official spokesman said.