Leave campaigners also say that Turkish membership will also cost NHS maternity services £400million in a decade.
Mr Cameron hit back within the hour during an interview on the Peston On Sunday show on ITV.
The Prime Minister said: “The Leave campaign is making a very misleading claim.”
Mr Cameron said Ms Mordaunt’s claims were “absolutely wrong.”
He added: “Britain and every other country in the European Union have a veto on another country joining.
“That is a fact, and the fact that the Leave campaign is getting things as straightforward as this wrong should call in to question their whole judgment in making the bigger argument about leaving the EU.”
Pressed on whether Ms Mordaunt was qualified to be kept on as a minister, the Prime Minister said: “Her responsibilities are in the Ministry of Defence, she is doing a very good job.
But on this question of whether or not we have a veto, the leave campaign is wrong.