The issue of the US citizens who took asylum in Cuba made headlines last Friday, after President Donald Trump reversed the rapprochement between Washington and Havana that began two years ago, and set the return of those people as one of the conditions to resume bilateral dialogue.
"It was a grotesque spectacle straight from the Cold War", Rodriguez said in Vienna, during a tour of European countries, in a news conference broadcast live in Cuba.
On Friday, Trump announced that he would revoke the "one-sided deal" the previous administration made with Cuba, blocking individual USA travel and all economic transactions with government entities, until Havana releases all political prisoners, legalizes all political parties and schedules internationally supervised elections.
Numerous changes that President Barack Obama made to Cuban policy, including restoring diplomatic relations and re-establishing direct flight service, will remain under Trump's Cuba policy, which bars Americans and U.S. companies from any transactions that benefit the Cuban military.
Additionally, he said he plans to restrict American travel to the island, and freeze transactions with Cuban military forces.
He added, however, that they would inevitably hit USA companies and citizens by restricting their ability to invest in or travel to Cuba, while also hurting the Cuban people.
Still, Rodriguez said, the Cuban government had no intention of meeting Trump's demands, including extraditing USA fugitives from justice, like convicted cop killer Assata Shakur.
"It will wreak economic damage not just on Cuba's state companies but also on the cooperatives and private sector workers", he said. The island nation will never negotiate its independence and sovereignty, the Cuban foreign minister said.
Meanwhile, the partial rollback of the detente would fall flat with the majority of Americans, who supported the normalization of relations with Cuba, and with whom the country would continue working, Rodriguez added.
President Donald Trump has demanded that Cuba return a woman convicted in the murder of a New Jersey state trooper.
Rodriguez also made a parting shot at Trump, noting that someone who was elected promising innovation and "America First" ended up reverting to a failed Cold War policy, one that restricts the rights of USA citizens and harms USA business.