President Trump told a group of television news anchors at the White House on Tuesday that he would participate in this year’s general election debates, despite his misgivings about the commission that oversees them, according to two people with knowledge of his comments.

Mr. Trump also said he hoped that Rush Limbaugh, the right-wing talk radio star who this week announced a diagnosis of advanced lung cancer, would attend Tuesday’s State of the Union address. The president said he was interested in awarding Mr. Limbaugh the Presidential Medal of Freedom. On Tuesday evening during his address, Mr. Trump did just that, with the first lady, Melania Trump, presenting the medal to a surprised Mr. Limbaugh in the gallery.

In a jovial mood after Iowa Democrats botched Monday’s caucus vote count — a situation that Mr. Trump happily called a “fiasco” — the president held court for nearly two hours on Tuesday afternoon over a lunch of sole and soup in the State Dining Room. Vice President Mike Pence and Ivanka Trump also attended.

The conversation, an annual tradition for anchors, is off the record, but as in past years, multiple people described Mr. Trump’s remarks after the fact. Journalists from The New York Times were not invited and did not agree to those off-the-record terms.