Some of his “Daily Show” commentary about the president has been scathing, and personal. The day after the election, Mr. Minhaj described his anxieties about Mr. Trump’s policies toward Muslims, saying that his mother had asked if she would be allowed back into the United States after a foreign trip to visit relatives.

“The fact that I can’t tell her ‘yes’ with 100 percent certainty is heartbreaking,” Mr. Minhaj said. “That is my mom, and I need her back home. Because I love her — and she owes me $300.”

In a statement on Tuesday, Mr. Minhaj called it “a tremendous honor to be a part of such a historic event even though the president has chosen not to attend this year. SAD!”

”Now more than ever, it is vital that we honor the First Amendment and the freedom of the press,” Mr. Minhaj added.

Officials at the correspondents’ group say the dinner will be focused on promoting journalism, with the famed writers Carl Bernstein and Bob Woodward to present awards for White House reporting. Scholarships funded by the association will also be at the forefront.

Alec Baldwin, who caricatures Mr. Trump on “Saturday Night Live,” called Mr. Mason at one point to talk about the possibility of an appearance, according to two people familiar with the discussion. The actor would likely have appeared as himself, and not in his Trump guise, the people said, in part because “Saturday Night Live” would have to give permission for Mr. Baldwin to reprise the impression outside of the show.

But some journalists in the Correspondents’ Association felt that awarding a featured spot to Mr. Baldwin could inject a blunt partisanship into the proceedings. Would network news anchors, for instance, feel comfortable laughing along with Mr. Baldwin — live on camera — if no one from the White House administration was there to reciprocate?