Jimmy Fallon, the host of “The Tonight Show” on NBC, said on Sunday that he would make a donation in President Trump’s name to the Refugee and Immigrant Center for Education and Legal Services, a nonprofit that provides legal defense services to immigrant and refugee families in Texas.

Mr. Fallon made the announcement after the president criticized him on Twitter over a recent interview in The Hollywood Reporter. In it, Mr. Fallon said he regretted playfully running his fingers through Mr. Trump’s hair on his show in September 2016, weeks before the presidential election.

What Mr. Fallon thought would be a funny moment came to haunt him. His critics, and even fellow late-night hosts, pounced, accusing him of normalizing an extremist candidate. He also disappointed many viewers, who fled his show, which had been a late-night ratings success, and have not returned.

“It was definitely a down time,” Mr. Fallon told The Hollywood Reporter about the criticism he received after the encounter with Mr. Trump. “I made a mistake. I’m sorry if I made anyone mad. And, looking back, I would do it differently.”

Mr. Trump on Sunday accused Mr. Fallon of “whimpering” and told him to “be a man.”

“@jimmyfallon is now whimpering to all that he did the famous ‘hair show’ with me (where he seriously messed up my hair), & that he would have now done it differently because it is said to have “humanized” me — he is taking heat,” the president tweeted. “He called & said ‘monster ratings.’ Be a man Jimmy!”

About three hours later, Mr. Fallon responded by saying he would donate to the nonprofit group, known as Raices. He did not disclose how much he would donate.

A fund-raising page on Facebook for the organization has raised more than $20 million as of Monday morning, far more than the $1,500 the couple who started it initially had hoped to raise. Raices has said the donations will help pay for legal representation for immigrant children and parents in Texas who have been separated under the Trump administration’s “zero-tolerance” immigration policy.