“Despite our unambiguous agreement to all of his terms last night, you added new stipulations this morning, for the first time, most notably the requirement of videotaping the interview,” the Clintons’ legal team wrote in an email to Mr. Comer on Tuesday morning, which was obtained by The New York Times.

The move appeared to be an effort to prevent House Republicans from selectively releasing unflattering exchanges from their videotaped depositions.

Mr. Comer did not acknowledge the request in his response.