Newt Gingrich, the former speaker of the House, and the Fox News anchor Megyn Kelly got into a televised tiff on Tuesday night in which he accused her of being “fascinated with sex” for her reporting on allegations of unwanted advances and groping by the Republican presidential nominee, Donald J. Trump.

The bizarre exchange played out toward the end of an interview on Ms. Kelly’s news program, “The Kelly File.”

The discussion turned from who was ahead in the polls — Mr. Trump or the Democratic nominee, Hillary Clinton — when Mr. Gingrich, a Republican and staunch supporter of Mr. Trump, accused Ms. Kelly and the news media of paying a disproportionate amount of attention to allegations by 10 women that Mr. Trump had forcibly kissed or groped them.

Mr. Gingrich questioned why a speech Mrs. Clinton had given in Brazil to a bank that had paid her $225,000 was not also worthy of coverage.