“Going to Cuba should be like going to Costa Rica or going to France,” said Mr. Díaz, who has lived in the United States for 50 years. Speaking of Mr. Trump and Mr. Rubio, he said: “Those two were enemies and now they’re holding hands? That’s called dirty politics. Mr. Rubio was born here, has never stepped foot on the island and does not represent the Cuban people.”
Mr. Díaz acknowledged that most Cuban expatriates his age who arrived long ago still burn with the bitterness of the era when the Castro revolution confiscated land and businesses, forcing waves of people into exile.
That voting bloc in Cuban Miami largely supports Mr. Trump’s decision to curtail American travel to Cuba and prevent companies from doing business with Cuban military enterprises. But their influence has diminished as tens of thousands more Cubans arrive in Miami, eager to visit their family back home and send them packages and cash.
“I should be over on that corner,” Mr. Díaz said, pointing across the street. “But I’m here on this side, because I have a heart and I have a brain.”
In yet another pendulum swing of American-Cuba policy, Mr. Trump on Friday dialed back some of the measures put in place by President Barack Obama. In moves that even the experts who supported Mr. Obama’s decision acknowledged stretched the limits of federal law, Mr. Obama had allowed Americans to travel more freely. He also permitted cruise ships, airlines and hotels to make deals in Cuba and re-established diplomatic relations with the former Cold War enemy.
Before Mr. Obama took office, Cuban exiles were allowed to visit the island only once every three years and were limited in how much money they could send home.
Perhaps in a signal of Cuban exiles’ diminishing influence over national policy, Mr. Trump did not change the rules for Cuban exiles to visit the island, nor did he cap the amount of money Cubans could send to their relatives. The new rules prevent visiting Americans from staying in hotels run by the military — which is most of them — and forces them to go to Cuba in organized groups.
That puts companies like the Marriott, which has a hotel in Cuba, on shakier ground.
“Americans can still go to Cuba?” said Robert Linares, 47, a warehouse manager who carried a sign here Friday criticizing the Castro government. “That’s not right. I want to see Trump do more. You can’t do business with an assassin or a criminal.”
Beside him stood Gustavo Falcón, 76, who offered anyone who would listen a history of the downfall of left-wing dictatorships. He questioned Mr. Obama’s rationale that opening Cuba to travel and business would somehow help bring about the government’s demise.
“Did any dictatorships that you know of collapse for economic reasons?” Mr. Falcón said. “Mr. Obama’s policies were economic measures trying to help them not collapse. Everything he did helped the military. All those private restaurants and hotels in Cuba are owned by them. I want to see Trump go a little bit further and wipe out everything Obama did.”
People around Mr. Falcon chanted Mr. Trump’s name, while hecklers shouted in unison that he was not their president. The police looked the other way while some of the protesters climbed over metal railings to goad one another up close.
“I was born in Cuba, and I want what’s best for Cuba,” Elena Freyre, a longtime activist against the trade embargo, said as a Trump supporter jeered at her.
“Where is the police?” she said. “This is going to get ugly if this is allowed to continue.”
After Mr. Trump’s speech, a group of Cuban exile activists — and a few dissidents who still live on the island — gathered nearby to thank the president for supporting their cause. They were jubilant as they described their disgust for Mr. Obama’s willingness to make deals and even attend a baseball game with Cuban leader Raúl Castro.
“Trump called the tyrant by his name: he is a dictator,” said Miriam de la Peña, whom Mr. Trump mentioned during his speech. “Raúl Castro is a dictator; he’s actually a murderer. He ordered the murder of my son, an American, who was at sea in international air space saving lives. And he’s out there shaking hands with our president? No way.”
Ms. de la Peña’s son, Mario, died in 1996 when the Cuban government shot down two rescue planes operated by Brothers to the Rescue, an exile rescue organization. Silvia Iriondo, a longtime activist who was aboard one of the planes that escaped, said she was touched that the president mentioned the victims by name.
“We expected less,” Ms. Iriondo said. “This new policy is geared toward depriving the Cuban government of resources it uses to beat, repress, incarcerate and get rich.”