Rishi Sunak is facing calls to apologise for a jibe about Sir Keir Starmer's position on trans people at Prime Minister's Questions.
The prime minister ridiculed the Labour leader for U-turning on the "definition of a woman".
Sir Keir was visibly furious, saying: "Of all the weeks to say that when Brianna's mother is in this chamber."
But Downing Street said it was "legitimate" to question Sir Keir's position on transgender issues.
Asked if the prime minister's comment was transphobic, his press secretary said: "I don't accept that at all."
Brianna Ghey's mother Esther was not in the public gallery for the exchange but entered shortly afterwards.
Later, Mr Sunak ignored a call from Labour MP Liz Twist to "apologise to Brianna Ghey's mother".
But at the end of the session the prime minister said Ms Ghey represented "the very best of humanity" for the "compassion" she showed after her 16-year-old daughter, who was transgender, was murdered by two teenagers who had a fascination with violence.
Reeling off a list of what he said were Labour U-turns, Mr Sunak said Sir Keir had changed his position on "defining a woman - although in fairness, that was only 99% of a U-turn".
His comments referred to an interview where Sir Keir had said "99.9% of women haven't got a penis".
Sir Keir hit back, saying: "Of all the weeks to say that, when Brianna's mother is in this chamber. Shame.
"Parading as a man of integrity when he's got absolutely no responsibility."
Later a spokeswoman for Sir Keir said: "We don't think the country wants or deserves a prime minister who is happy to use minorities as a punch bag.
"The comments were deeply offensive to trans people. He should reflect on his response there and apologise."
However, Minister for Women and Equalities Kemi Badenoch said it was "shameful" of Sir Keir "to link his own inability to be clear on the matter of sex and gender" to Ms Ghey's grief.
"Every murder is a tragedy. None should be trivialised by political point-scoring," the Tory MP wrote on X.
Chancellor Jeremy Hunt denied Mr Sunak had made a minority group "a punchline for a joke" and declined to say whether he thought the PM should apologise.
"The prime minister could not have been clearer about the enormous respect that he has for Brianna Ghey's mother," he told the BBC.
"What he was saying is that on the really important issues of the day Labour and Sir Keir Starmer simply cannot make up [their] mind."
Ms Ghey was in the Houses of Parliament to attend a debate on mindfulness in schools, organised by her local MP Charlotte Nichols.
She also met Sir Keir after Prime Minister's Questions.
Mr Sunak had been told Ms Ghey was in the public gallery watching PMQs but she had missed the opening exchanges, coming into the session about 15 minutes after it started.
The PM's spokesperson would not say whether a government minister was meeting Ms Ghey whilst she was visiting Parliament. Ms Ghey did briefly talk with Education Secretary Gillian Keegan after they both appeared on the BBC's Sunday with Laura Kuenssberg.
At the end of the session, with Ms Ghey seated in the gallery, Mr Sunak repeated previous comments that the murder of Brianna "was an unspeakable and shocking tragedy".
Ms Ghey "deserves all our admiration" for showing "empathy" for the family of her daughter's killers, he added.
Brianna was murdered after being lured to a park near her home by a school friend, in a stabbing partially motivated by hostility towards Brianna because she was transgender.
SNP MP Hannah Bardell later tried to use parliamentary rules to force Mr Sunak back to the Commons to apologise for making a "transphobic joke" during LGBT History Month.
Ms Bardell accused politicians and the media taking part in "unprecedented attacks" on the trans and non-binary community.
Deputy Speaker Dame Eleanor Laing said she could not compel Mr Sunak to apologise, but advised MPs that "when a tragedy has occurred we ought to show sympathy and understanding and not always make political points".
Liberal Democrat deputy leader Daisy Cooper MP said: "People are not a punchline - and it's long overdue that the prime minister learns that. The British public, and Brianna's mother, deserve so much more than this."