The search warrant carried out by the public corruption unit of the Manhattan federal attorney’s office seeks information about Karen McDougal, an ex-Playboy model who claims she carried on a nearly yearlong affair with Mr. Trump shortly after the birth of his son in 2006. Ms. McDougal was paid $150,000 by American Media Inc., the Enquirer’s parent company, whose chief executive is a friend of Mr. Trump’s.

Agents were also searching Michael D. Cohen’s office for information related to Stephanie Clifford, better known as Stormy Daniels, who says she also had sex with Mr. Trump while he was married. Mr. Cohen has acknowledged that he paid Ms. Clifford $130,000 as part of a nondisclosure agreement to secure her silence just days before the 2016 presidential election.