Puerto Rico’s Republican Party chairman said on Monday that he would withhold his support from former President Donald J. Trump unless he apologized for racist remarks that an insult comic made about the U.S. territory on Sunday during Mr. Trump’s rally at Madison Square Garden.

While residents of U.S. territories are not eligible to vote for president, Angel M. Cintrón, the island’s G.O.P. chairman, called on Mr. Trump to personally disavow comments made by the comic, Tony Hinchcliffe, in an opening speech at his rally that referred to Puerto Rico as a “a floating island of garbage.”

Otherwise, Mr. Cintrón said during a talk show appearance, he would not be casting a symbolic ballot in the election for Mr. Trump, whose nomination he helped cement in July during a roll call at the Republican National Convention in Milwaukee when Puerto Rico awarded all 23 of its G.O.P. delegates to the former president. (Puerto Ricans are American citizens, and they are eligible to vote as residents in states. A sizable number of Puerto Ricans live in Pennsylvania, a crucial battleground state.)

The Trump campaign did not immediately respond to a request for comment on Monday night.

Earlier, Danielle Alvarez, a senior adviser to the Trump campaign, said in a statement that the Puerto Rico joke “does not reflect the views of President Trump or the campaign.”

But in a letter to Mr. Trump posted on social media on Monday night, the archbishop of San Juan, P.R., Roberto O. González Nieves, said the explanation fell short.

“It is not sufficient for your campaign to apologize,” he wrote. “It is important that you, personally, apologize for these comments.”

In his letter, the archbishop wrote that Mr. Hinchcliffe’s remarks “not only provoke sinister laughter but hatred.”

Mr. Trump made a rare apology on Friday night when he kept supporters at a rally in Michigan waiting in the cold for more than two hours as he taped a three-hour episode for Joe Rogan’s podcast.

By and large, the former president is not known for his contrition. In 2018, when Mr. Trump was facing criticism over an aide’s joke that Senator John McCain was irrelevant because he would soon die, a Republican strategist, Kevin Madden, said, “The president has always throughout his career had a stance of ‘never apologize, never back down.’”