Carmen Yulín Cruz’s cellphone started buzzing on Sunday while she was at the airport in Connecticut, waiting for a flight to Puerto Rico. A standup comic at former President Donald J. Trump’s rally in New York had called Puerto Rico a “floating island of garbage.”

As video clips of the comic, Tony Hinchcliffe, began flashing on airport televisions, fellow Puerto Ricans preparing to board their flight began erupting, Ms. Cruz said.

“People were asking me, ‘Mira, Yulín, what is this guy saying?’ — only in more colorful language,” Ms. Cruz, the former mayor of San Juan, Puerto Rico’s capital, said on Monday. “And I said: ‘Well, this isn’t the first time. Let’s not be surprised.’”

As president, Mr. Trump fought bitterly with Ms. Cruz and other Puerto Rican leaders, and resisted sending billions of dollars in aid after the territory was ravaged by back-to-back hurricanes in 2017. He made angry comments on social media and tossed paper towels at Puerto Ricans during a visit that few, if any, have forgotten. He even wondered privately if the United States could sell the island.

In 2019, Mr. Trump decried local leaders as “grossly incompetent.” A year later, while running for re-election, he tried to portray himself as the “best thing that ever happened” to the island. The Republican Party platform no longer mentions statehood for Puerto Rico, a position the party had held before Mr. Trump’s relationship with the island soured.

While his campaign distanced itself from Mr. Hinchcliffe’s joke, saying it did not reflect Mr. Trump’s views, Mr. Trump himself has not apologized.

“You have to understand the context of how hurtful this is by understanding the botched and deadly response to Hurricane Maria,” said Representative Darren Soto, a Florida Democrat of Puerto Rican descent. “This is also clearly discrimination.”

Over the years, Mr. Trump has viewed Puerto Rico through little more than a political lens, seemingly frustrated by a territory that has required significant federal help to recover from bankruptcy, hurricanes and earthquakes.

The incident on Sunday prompted fierce backlash in Puerto Rico and across its vast diaspora, including politicians and celebrities such as Bad Bunny. Archbishop Roberto O. González Nieves of San Juan wrote an open letter to Mr. Trump on Monday.

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

Also on Monday, the chairman of Puerto Rico’s Republican Party said that he would withhold his support from Mr. Trump unless he apologized.

Some Puerto Ricans drew parallels between the campaign’s giving Mr. Hinchcliffe a platform to make racist jokes and Mr. Trump’s spreading false claims, with his running mate, Senator JD Vance of Ohio, that Haitian residents of Springfield, Ohio, were stealing and eating pets.

“It’s just another day in Trump world,” Marcos Vilar, a Puerto Rican who is the executive director of Alianza for Progress, a Latino advocacy group in Florida, said at a news conference on Monday in Kissimmee, a heavily Puerto Rican city south of Orlando.

Puerto Ricans are American citizens, and while the 3.2 million who live on the island cannot vote for president, those who live in U.S. states — about 5.8 million — can. They tend to lean Democratic, though their turnout has often been relatively low compared with their population. In recent elections, Republicans won over some Puerto Ricans, part of a broader trend with Hispanic voters.

Bob Cortes, a Puerto Rican Republican and former state representative from Central Florida, said he could see Puerto Rican voters who had been undecided in the presidential election being swayed by what happened on Sunday. Mr. Cortes said that he was “disappointed” by the incident but that he remained a Trump supporter.

“A lot of people complain about the withholding of funds” by Mr. Trump after Hurricane Maria devastated the island in 2017, Mr. Cortes said. “He withheld some of the funds to hold some of those who were misusing the funds in Puerto Rico accountable.”

Puerto Rico’s reconstruction has been far slower than in states like Florida and Texas, which were also struck by disasters in 2017, in part because the Trump administration placed restrictions on aid for Puerto Rico that did not apply to other jurisdictions. Congress provided $20 billion to the Department of Housing and Urban Development for Puerto Rico after Maria; only $138 million had been spent by the time President Biden took office and released more of the funds.

Puerto Ricans acknowledge that they have had some poor elected leaders. Federal authorities have secured a slew of public corruption convictions in recent years against legislators and mayors.

But Puerto Ricans do not take mocking lightly. Gov. Ricardo A. Rosselló, a Democrat who was in charge during Hurricane Maria, was forced to resign in 2019 after weeks of protests. The demonstrations began after leaked messages from a private group chat showed Mr. Rosselló and associates of his, all men, ridiculing women, gay people, obese people, political opponents and even some of their supporters.

“People have a big mistrust in government as a whole, coming from Puerto Rico,” Mr. Cortes said.

Ms. Cruz, the former San Juan mayor and a Democrat, said Mr. Hinchcliffe’s remark at the rally made her heart sink. Moments from the aftermath of Hurricane Maria replayed in her head, she added. After the storm, Mr. Trump called Ms. Cruz “nasty,” which raised her profile as a Trump critic.

Ms. Cruz, like other Puerto Ricans, blamed the Trump administration for at least some of the many deaths on the island after Maria, which were caused in part by lack of electricity and medical care.

Three thousand Puerto Ricans died because he weaponized the aid,” she said. “Because he didn’t think our lives were worth saving, and because of his inability to do his job.”

“And it was painful,” she added about hearing Puerto Ricans insulted once again, “because you think, ‘My God, it’s not like this person hasn’t showed who he is to the world.’”

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