When President Trump attended a fund-raiser at a private home in Beverly Hills on Tuesday night, there was a familiar face in the crowd: Thomas J. Barrack Jr., the billionaire investor and an old friend of the president’s who has come under scrutiny by federal prosecutors looking into possible foreign influence over Mr. Trump’s 2016 campaign.

Mr. Barrack was among Mr. Trump’s relatives, party and campaign officials and the well-heeled attending the event at the home of Geoffrey Palmer, a real estate developer, according to two people familiar with what took place. Mr. Barrack spoke during the round-table portion of the event, and the president acknowledged him pleasantly, one of the people said.

Mr. Barrack also attended a fund-raising breakfast for Mr. Trump on Wednesday morning in Los Angeles. And he has given $360,600, the maximum amount allowable, to the Trump Victory Committee, a joint entity between the Trump campaign and the Republican National Committee, according to three people familiar with the donor list.

As federal prosecutors examine the presidential inaugural committee, which Mr. Barrack led, and possible lobbying efforts by foreign governments looking to influence the new administration, Mr. Barrack is sending signals that the attention on him has not deterred his interest in engaging in the 2020 campaign.