Republicans on Capitol Hill presented a cake to Donald J. Trump on Thursday and serenaded him for his 78th birthday. He is scheduled to spend Friday, his actual birthday, in Palm Beach, Fla., with a group of supporters, led by three Florida residents, called Club 47 USA.

Mr. Trump may be even more at ease with this group, which describes itself as “a corporation formed to support the agenda and re-election” of the former president, than he is with congressional Republicans. In October, Mr. Trump opened up to these supporters about the day during his presidency that the United States decided to move ahead with a drone strike on Iran’s top security and intelligence commander, Maj. Gen. Qassim Suleimani.

“Nobody’s heard this story before,” Mr. Trump had said to the group. “But I’d like to tell it to Club 47, because you’ve been so loyal.” He told them how disappointed he had been with Prime Minister Benjamin Netanyahu of Israel on that day in 2020 — even though he was talking to the group only four days after the deadly Oct. 7 attack led by Hamas on the country.

“I’ll never forget that Bibi Netanyahu let us down,” Mr. Trump told the group.

Mr. Trump has indicated mixed feelings about his own birthday.

At his rally on Sunday in Las Vegas, when someone seemed to wish him a happy birthday onstage, he said he didn’t want to hear it. The crowd began singing to him anyway.

“You know there’s a certain point at which you don’t want to hear ‘Happy birthday.’ You just want to pretend the day doesn’t exist, but anyway,” he said, before pointing out that his parents had both lived a long time.

The birthday celebration that Club 47 USA has planned on Friday will take place at a convention center down the road from Mar-a-Lago. Mr. Trump is expected to speak at 7 p.m.