During the interview on Wednesday, she was shown a clip of a past interview on LBC in which Sir Keir appeared reluctant to say whether women can have penises.
Ms Duffield, asked for her reaction to Sir Keir being ‘unable to say whether people with penises are women’, said: ‘Speechless really.
Mr Starmer has previously said, when posed with anatomical questions on trans issues, that he did not think that ‘discussing this issue in this way helps anyone in the long run’.
He recently spoke about his concerns over the Scottish Parliament’s Bill lowering the age someone can legally change their gender from 18 to 16.
The Gender Recognition Reform (Scotland) Bill was blocked by the UK Government after it was deemed to interfere with Westminster-set equalities legislation.
Ms Duffield has faced both abuse and praise for standing up for women’s rights and women’s spaces in the debate over transgender rights.
She said Sir Keir phoned her when the level of abuse became ‘really bad’ but said he ‘won’t show public support’ for her.
The politician put the party hierarchy’s decision not to offer her position support down to Labour being led by a number of senior male figures.