CORAL GABLES, Fla. — The Trump administration on Wednesday intensified its crackdown on Cuba, Nicaragua and Venezuela, rolling back Obama administration policy and announcing new restrictions and sanctions against the three countries whose leaders national security adviser John Bolton dubbed the "three stooges of socialism."

"The troika of tyranny — Cuba, Venezuela and Nicaragua — is beginning to crumble," Bolton said in a hard-hitting speech near Miami on the 58th anniversary of the United States' failed Bay of Pigs invasion of the island, an attempt to overthrow the Cuban government.

The measures seem likely to hit hardest in Cuba, which is at a moment of severe economic weakness as it struggles to find cash to import basic food and other supplies following a drop in aid from Venezuela and a string of bad years in other key economic sectors.

Bolton announced a new cap on the amount of money that families in the United States can send their relatives in Cuba. The Obama administration had lifted limits on remittances, but the new limit will be $1,000 per person per quarter. Remittances to Cuba from the United States amounted to $3 billion in 2016, according to the State Department.

Washington also moved to restrict "non-family travel" after a broad loosening of so-called purposeful visits under Obama led to soaring numbers of American trips for cultural and educational exchanges. Details on the restrictions were not immediately clear, but tourism is a key lifeline of hard currency for Cuba. Bolton called such visits "veiled tourism."

Bolton spoke hours after Secretary of State Mike Pompeo announced a new policy allowing lawsuits against foreign firms operating on properties Cuba seized from Americans after the 1959 revolution. The United States has enforced a trade embargo against Cuba since the early 1960s.

Cuban officials met the announcements with defiance.

"Nobody will snatch away from us, neither through seduction nor force, 'the Fatherland that our parents won for us by standing up,'" President Miguel Díaz-Canel said via Twitter. "We Cubans will not surrender."

Foreign Minister Bruno Rodríguez called it an attack on international law, Cuban sovereignty and countries that would do business with the island: "Aggressive escalation by (hashtag)US against Cuba will fail. Like at Giron, we will be victorious," he tweeted, referring to a Bay of Pigs beach where invaders landed.

On Venezuela, Bolton said Washington was sanctioning the country's Central Bank, which the Trump administration says has been instrumental in propping up the embattled government of President Nicolás Maduro. He also announced sanctions against financial services provider Bancorp, which he claimed is a "slush fund" for Nicaraguan President Daniel Ortega.

"The United States looks forward to watching each corner of this sordid triangle of terror fall: in Havana, in Caracas, and in Managua," Bolton said in South Florida, which is home to many thousands of exiles and immigrants from the three countries.

He said Obama administration policies had given the Cuban government "political cover to expand its malign influence" across the region, including in Venezuela. Cuba has trained Venezuelan security forces to repress civilians and support Maduro, Bolton said, calling Maduro "quite simply a Cuban puppet."

Bolton's pledge to "never, ever abandon" the people of Cuba, Venezuela and Nicaragua in their fight for freedom also might ring hollow in light of the historical events he sought to highlight at the event hosted by the Bay of Pigs Veterans Association.

Many Cuban Americans to this day resent the late President John F. Kennedy for not deploying American troops at a critical moment in the Bay of Pigs invasion.

Meanwhile, with the high stakes of the Cold War a fading memory, some critics of U.S. policy toward Venezuela worry that the Trump administration's stance that all options are on the table, including a military one, to oust Maduro is an empty threat that will only serve to ignite the streets and geopolitical tensions with Russia, compounding the misery of Venezuelan citizens.

"Honoring one of U.S.' greatest military fiascos from 60 years back suggests U.S. policy to Latin America owes more now to a perverse Cold War nostalgia than practical benefits for people of the region," said Ivan Briscoe, the Latin American director for the International Crisis Group, a Brussels-based think tank.

Collin Laverty, president of Cuba Educational Travel, said in a statement that the measures on remittances and travel threaten the economic survival of Cuban families and the viability of thousands of independent small businesses allowed to operate since 2010 under reforms implemented by former President Raúl Castro.

"The only winners here are a handful of members of Congress and those stuck in the past that support them," Laverty said. "The losers are millions of Cubans on and off the island and the overwhelming majority of Americans that support engagement with Cuba."

Many of the 400 or so who paid $100 to attend Bolton's speech at the Biltmore in South Florida were of Cuban descent. Rafael UsaTorres, a member of the 2506 Brigade that worked for the CIA at the time of the invasion, said he has faith that the measures will bring down Díaz-Canel's government, though he wished it had been done sooner.

"Today is a big day," the 78-year-old said. "But I feel very sad — Too many years waiting."

But others said Washington isn't going far enough. Manuel Menendez-Pou, 79, said the Cuban government had confiscated some $63 million in property from his family, once one of the wealthiest on the island, mainly in the sugar industry.

"The problem is not the money," Menendez-Pou, also a former member of the brigade said minutes before the speech. "They stole our life."

In Havana, homemaker Odalis Salazar worried about the future of remittances she receives from two children living abroad, including one in the United States.

"It hurts everyone and Trump is absolutely criminal, because he knows that ... (the remittances) help us a lot," Salazar said. "We Cubans have families there and we get by largely with that help that they send us."

"We have already gone through other periods of crisis and we overcame them," said Tania Astiazarain, a guide at the Playa Giron museum. "This does not scare us, and we are prepared for whatever comes."

Pompeo's decision on allowing lawsuits lets Americans, including Cubans who became naturalized citizens years after the fact, sue companies that operate out of hotels, tobacco factories, distilleries and other properties nationalized after Fidel Castro took power.

Pompeo said he would not renew a bar on litigation that has been in place for two decades, meaning that lawsuits can be filed starting May 2 when the current suspension expires.

The Justice Department has certified roughly 6,000 claims as having merit, according to Kimberly Breier, the top U.S. diplomat for the Americas. Those claims have an estimated value of $8 billion: $2 billion in property and $6 billion in interest, she said. Another 200,000 uncertified claims could run into the tens of billions of dollars, she said.

Breier said there would be no exceptions to the policy but foreign companies "will have nothing to worry about if they are not operating on properties taken from Americans."

Nonetheless, companies in the European Union and Canadian companies stand to lose tens of billions in compensation and interest, and the decision prompted stern responses and vows to protect businesses from lawsuits.

In a statement, EU foreign policy chief Federica Mogherini and Canadian Foreign Minister Chrystia Freeland called the decision to remove the longstanding waivers "regrettable" and said it "can only lead to an unnecessary spiral of legal actions."

In Spain, which has large investments in hotels and other tourism-related ventures on the island, a senior government official said Madrid would ask the EU mount a challenge at the World Trade Organization.

"The extraterritorial application of the U.S. embargo is illegal and violates international law," said Alberto Navarro, EU ambassador to Cuba. "I personally consider it immoral. For 60 years the only thing that's resulted from the embargo is the suffering of the Cuban people."

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Associated Press writers Michael Weissenstein in Miami, Andrea Rodríguez in Havana and Aritz Parra in Madrid contributed to this report.