European Union foreign policy chief Federica Mogherini and trade commissioner Cecilia Malmstrom sent the warning in a letter dated April 10 to US Secretary of State Mike Pompeo, according to the letter obtained by AFP.
In a joint statement, the EU's High Representative for Foreign Affairs, Federica Mogherini, and Trade Commissioner Cecilia Malmstrom expressed "strong opposition to the extraterritorial application of unilateral Cuba-related measures that are contrary to worldwide law".
The administration of US President Donald Trump says it will impose sanctions on Venezuela's central bank, while criticizing Russian Federation and Cuba for backing Venezuelan President Nicolas Maduro.
In a hard-hitting speech in Miami largely devoted to Cuba, National Security Advisor John Bolton also unveiled measures against a third leftist government in Latin America, Nicaragua, with sanctions against President Daniel Ortega's son.
He says the new measures will help steer US dollars away from the Cuban government, its military or its security services.
"Our respective laws allow any United States claims to be followed by counter-claims in European and Canadian courts", the three officials said.
"Sometimes regimes that look alike are treated differently because in the constellation of American interest, our relationship with them and the circumstances we face is different, and I don't think we need to make any apologies for that - not this administration, or not other administrations".
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When asked if the USA would allow any exemptions under the decision, specifically with regard to U.S. companies doing business in Cuba, State Department official Kimberly Breier said, "There will not be any exemptions". The epic Cold War clash saw Fidel Castro's forces repel about 1,500 Cuban exiles who had been trained and armed by the Central Intelligence Agency with the aim of overthrowing the communist government that had taken over a country just 135 kilometres off Florida's southern tip two years earlier.
With regard to Venezuela, Bolton said the state's central bank had been crucial to Maduro's continued rule and that the sanctions imposed on it "should be a strong warning to all external actors, including Russian Federation, against deploying military assets to Venezuela to prop up the Maduro regime".
In a Miami speech last November, just before the US midterm elections, Bolton referred to the three countries as the "Troika of Tyranny".
In response to the intensification of USA pressure on Cuba, the European Union on Wednesday warned the United States against potential moves that would impact European interests in Cuba.
"Our respective laws allow any USA claims to be followed by counter-claims in European and Canadian courts, so the US decision to allow suits against foreign companies can only lead to an unnecessary spiral of legal actions".
The EU has reacted angrily to a Trump administration announcement that Americans to sue foreign firms over seized Cuban property, threatening to take a case to the World Trade Organisation.
"Those citizens' opportunities for justice have been put out of reach for two decades", Pompeo said.
The Trump administration on Wednesday opened the door for lawsuits against foreign firms operating on properties Cuba seized from Americans after the 1959 revolution.
The move comes as the Trump administration attempts to ratchet up the pressure on Nicolas Maduro's regime in Venezuela and countries that they see as sustaining it.