Former President Donald J. Trump declared himself the “father of I.V.F.” in a town-hall event Tuesday focused on women’s issues, an eyebrow-raising nickname that was his latest attempt to claim an advantage on a matter that has become a political liability.

The Supreme Court justices Mr. Trump appointed enabled the overturning of Roe v. Wade, a ruling that he has praised and that opened the door to possible restrictions on in vitro fertilization.

“We really are the party for I.V.F.,” Mr. Trump said in the town hall, which was hosted by Fox News and aired on Wednesday. He has expressed support for I.V.F. in recent months, but he did not discuss or promote it before this year.

“We want fertilization, and it’s all the way, and the Democrats tried to attack us on it, and we’re out there on I.V.F., even more than them,” he said.

Congressional Republicans have voted twice in the past four months to block bills that would protect the legality of I.V.F., including one that would also guarantee insurance coverage of it, which Mr. Trump has said he wants to do.

Karoline Leavitt, a spokeswoman for the Trump campaign, said the “father of I.V.F.” remark was “a joke President Trump made in jest when he was enthusiastically answering a question about I.V.F.” She did not respond when asked twice whether Mr. Trump supported the bill that Republicans had blocked.

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