President Trump personally directed an effort in February to stop Stormy Daniels from publicly describing an alleged sexual encounter with Mr. Trump, people familiar with the events say.

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 this year’s 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.

Mr. Trump on Tuesday declined to answer questions about whether he had directed his son and Mr. Cohen to pay Ms. Clifford earlier this year, telling reporters “I don’t even know what you’re talking about.”