“There are no troops,” Carlos Fernández de Cossío, Cuba’s director general of U.S. affairs, told the Associated Press in Washington on Wednesday. “Cuba does not participate in military operations nor in security operations in Venezuela.”

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Accusations of foreign involvement in Venezuela’s crisis are not new from either side. After the failure of the uprising on Tuesday, Secretary of State Mike Pompeo suggested that Russian officials had persuaded Maduro to stay put instead of fleeing. Venezuelan officials have accused the United States of backing a “coup” attempt organized by Guaidó.

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But the allegation about Cuban security forces in Venezuela would seem easier to prove or disprove — after all, how do you hide 20,000 to 25,000 soldiers?

Former U.S. officials say there may be a gray area. “It’s hard to say what’s what,” said Fernando Cutz, who was a senior adviser to then-national security adviser H.R. McMaster and served as South America director in the National Security Council. “The truth is likely somewhere in the middle.”

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The ambiguity notwithstanding, President Trump has threatened to impose a full embargo and high-level sanctions on Cuba over the alleged Cuban troop presence in Venezuela. “Hopefully, all Cuban soldiers will promptly and peacefully return to their island!” Trump tweeted Tuesday.

In response, Cuban Foreign Minister Bruno Rodríguez Parrilla accused the United States of outright falsehoods about Cuba’s role in Venezuela, describing Bolton as a “pathological liar who misinforms Trump.”

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There are no Cuban soldiers in Venezuela, Rodríguez tweeted Tuesday, nor Cubans taking part in any military or security operations there. “Only medical staff in humanitarian mission,” he said.

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Cuba has a long-standing agreement with Venezuela to trade temporary workers for billions of dollars in oil. By most reports, upward of 20,000 Cubans are indeed in Venezuela, but Havana says many of them are doctors and nurses, part of Cuba’s system of exporting its well-trained medical workers all over the world in exchange for cash and other benefits.

Johana Tablada, de Cossío’s deputy, told reporters in Havana this week that all Cubans in Venezuela are civilians and that 94 percent of them work in medical missions. (Recent estimates suggest that Cuba’s armed forces may number as low as 40,000.)

But accounts from former Venezuelan military officials suggest that Cubans play a significant role in the Venezuelan armed forces. In an interview with The Washington Post in March, one former lieutenant colonel in the Venezuelan army who fled to the United States in 2018 said Cubans dressed in civilian clothing acted as “our supervisors and decision-makers.”

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Cuban doctors in Venezuela have been accused of using medical care to compel patients to vote for Maduro ahead of last year’s presidential election.

Even so, the exact influence of Cuba on Venezuela is hard to gauge. “There is no doubt that Cubans are very much assisting the Venezuelan regime — the Maduro regime — to stay in power,” said Cutz, the former NSC official.

Is their presence so strong that if they left, Maduro’s regime would collapse? Cutz said he wasn’t so sure. “We never had to have those conversations,” he said of his time working in the Trump administration, which he and McMaster left a year ago.

Supporters of the administration’s Venezuela policy, such as Sen. Marco Rubio (R-Fla.), would dispute this. Responding to a New York Times story that reported that a CIA assessment concluded Cuba was not as involved in Venezuela as the administration believed, Rubio said the reporters were being “lied to.”

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No U.S. agency doubts that Cuba is in “effective control of Venezuela security forces,” Rubio tweeted Thursday morning. But the senator and others making similar claims have offered no evidence — a detail that Cuban officials have repeatedly highlighted.

“I invite them to provide evidence,” Rodríguez said last week during a news conference in Havana. “I invite them to provide proof.”