In a phone call, Mr. Trump instructed his then-lawyer Michael Cohen to seek a restraining order against the former adult-film actress, whose real name is Stephanie Clifford, through a confidential arbitration proceeding, one of the people said. Messrs. Trump and Cohen had learned shortly before that Ms. Clifford was considering giving a media interview about her alleged relationship with Mr. Trump, despite having signed an October 2016 nondisclosure agreement.

Mr. Trump told Mr. Cohen to coordinate the legal response with Eric Trump, one of the president’s sons, and another outside lawyer who had represented Mr. Trump and the Trump Organization in other matters, the people said. Eric Trump, who is running the company with his brother in Mr. Trump’s absence, then tasked a Trump Organization staff attorney in California with signing off on the arbitration paperwork, these people said.

Direct involvement of the president and his son in the effort to silence Ms. Clifford hasn’t previously been reported. The accounts of that effort recently provided to The Wall Street Journal suggest that the president’s ties to his company continued into this year and contradict public statements made at the time by the Trump Organization, the White House and Mr. Cohen.