Havana, Cuba - Talks between Cuba and the US on de-escalating tensions are still at a "very preliminary" stage, Cuba's Deputy Foreign Minister Josefina Vidal told AFP on Tuesday.

Cuba has been bracing for a possible US attack following threats from President Donald Trump about "taking" the communist-run island after ousting Venezuela's leader and attacking Iran.

The former Cold War rivals have, at the same time, held exploratory talks.

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"We are in a very preliminary, very initial phase, and there are still no structured negotiations between the two governments," Vidal told AFP during a demonstration in Havana to denounce the impact of US sanctions on the impoverished island.

Trump effectively shut down oil exports to Cuba in January after US forces ousted Havana's main regional ally and crude supplier, Venezuela's Nicolas Maduro.

Trump also threatened tariffs on other countries that ship oil to Cuba, deepening an energy crisis on the island marked by recurring blackouts.

Last week, however, Washington allowed through a Russian oil tanker.

Vidal (65) was a key figure in the restoration of relations between Washington and the communist-run island during Barack Obama's presidency in 2015.

In February, the Miami Herald listed her as one of Secretary of State Marco Rubio's interlocutors, along with Raul Guillermo Rodriguez Castro, grandson of former president Raúl Castro.

Cuba has taken apparent steps in recent weeks to ease tensions, notably releasing groups of prisoners in two batches, in what it called a "humanitarian gesture."

Last week, it announced the pardon of more than 2,000 prisoners. However, none of these were political prisoners, according to human rights NGOs.

At least 20 political prisoners were released in mid-March.

Vidal contrasted the current talks with the negotiations between the Obama and Raúl Castro administrations, which led to an historic rapprochement that Trump later walked back.

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In 2015, "we worked to create a relationship that was not without differences, but that did not place those differences at the center," Vidal stressed.

She insisted however that "Cuba has always believed in dialogue" and "not in confrontation."