Bill Maher will win the prestigious Mark Twain prize for American humor, the Kennedy Center said Thursday, less than a week after the White House forcefully denied that the comedian, who has had a hot-and-cold relationship with Donald Trump, would win it.

“For nearly three decades, the Mark Twain prize has celebrated some of the greatest minds in comedy,” Roma Daravi, the Kennedy Center’s vice-president of public relations, said in a statement. “For even longer, Bill has been influencing American discourse — one politically incorrect joke at a time.”

Maher said in a statement that he “just had the award explained to me, and apparently it’s like an Emmy, except I win”.

After the Atlantic reported last week that Maher would win the award, the White House pushed back hard. Steven Cheung, the White House communications director, said on social media that the story was “literally FAKE NEWS”.

The White House didn’t immediately comment on the award on Thursday.

The Kennedy Center has presented the award since 1998 as a way to recognize those who have made significant contributions to humor and commentary in the United States. Previous winners include Conan O’Brien, Dave Chappelle, Julia Louis-Dreyfus, David Letterman, Carol Burnett and Tina Fey.

The award will be presented on 28 June, just before Trump plans to close the Kennedy Center for renovations expected to last about two years. Since returning to office, the Republican president has wielded tremendous influence over the venue, ousting its previous leadership and replacing it with a handpicked board of trustees that named him chairman.

The board added Trump’s name to the Kennedy Center and approved the closure, actions that have prompted legal proceedings that are ongoing.

Maher and the president have long had a fraught relationship.

Before he entered politics, Trump filed a $5m lawsuit against Maher in 2013 for breach of contract. Appearing on Jay Leno’s the Tonight Show, Maher said he would give $5m to the charity of Trump’s choice if he could prove he was not “the spawn of his mother having sex with an orangutan”.

Trump claimed that when he provided his birth certificate, Maher didn’t pay up, prompting the lawsuit. Trump ended up dropping it.

The Trump-Maher relationship exploded again earlier this year, when the president claimed on social media that he wasted time sitting down for a meal with the comedian last year.

“He came into the famed Oval Office much different than I thought he would be,” Trump wrote online. “He was extremely nervous, had ZERO confidence in himself.” Trump said the comedian admitted he was “scared”.

Maher described the dinner as a “good time” during his 11 April episode of Real Time, noting that Trump was “gracious and measured” and not like the “person who plays a crazy person on TV”. Maher said he wasn’t scared.

He took time in his New Rules segment to point out the various Trump policies he liked, including the “mass removal of stone cold criminals” and making Nato members pay “their fair share”.

“I may be the last person from the lunatic left that is still an honest broker when it comes to you,” he said. ”I always want the American president to succeed, and I do give credit when you have, but there’s lots of stuff you do that is not my idea of success, and I have every right to say so in a democracy.”