US President Donald Trump has ordered tighter restrictions on Americans travelling to Cuba and a clampdown on US business dealings with the island's military, saying he was cancelling former President Barack Obama's "terrible and misguided deal" with Havana.

Laying out his new Cuba policy in a speech in Miami, Trump on Friday signed a presidential directive to roll back parts of Obama's historic opening to the Communist-ruled country after a 2014 diplomatic breakthrough between the two former Cold War foes.

But Trump was leaving in place many of Obama's changes, including the reopened US embassy in Havana, even as he sought to show he was making good on a campaign promise to take a tougher line against Cuba.

"We will not be silent in the face of communist oppression any longer," Trump told a cheering crowd in Miami's Cuban-American enclave of Little Havana, including Republican Senator Marco Rubio of Florida, who helped forge the new restrictions on Cuba.

"Effective immediately, I am cancelling the last administration's completely one-sided deal with Cuba," Trump declared as he made a full-throated verbal assault on the government of Cuban President Raul Castro.

Trump's revised approach, which will be contained in a new presidential directive, calls for stricter enforcement of a longtime ban on Americans going to Cuba as tourists, and seeks to prevent US dollars from being used to fund what the Trump administration sees as a repressive military-dominated government.

But facing pressure from US businesses and even some fellow Republicans to avoid turning back the clock completely in relations with communist-ruled Cuba, the president chose to leave intact some of his Democratic predecessor's steps toward normalisation.

The new policy bans most US business transactions with the Armed Forces Business Enterprises Group, a Cuban conglomerate involved in all sectors of the economy, but makes some exceptions, including for air and sea travel. This will essentially shield US airlines and cruise lines serving the island.

"We do not want US dollars to prop up a military monopoly that exploits and abuses the citizens of Cuba," Trump said, pledging that US sanctions would not be lifted until Cuba frees political prisoners and holds free election.

However, Trump stopped short of breaking diplomatic relations restored in 2015 after more than five decades of hostilities. He will not cut off recently resumed direct US-Cuba commercial flights or cruise-ship travel.

The administration, according to one White House official, has no intention of "disrupting" existing business ventures such as one struck under Obama by Starwood Hotels Inc, which is owned by Marriott International Inc, to manage a historic Havana hotel.

Nor does Trump's plan reinstate limits that Obama lifted on the amount of the island's coveted rum and cigars that Americans can bring home for personal use.

Trump's aides contend that Obama's efforts had done nothing to advance political freedoms in Cuba, while benefiting the Cuban government financially.

Citing the lack of human rights concessions from Cuba in the detente negotiated by Obama, Trump said, "It's hard to think of a policy that makes less sense than the prior administration's terrible and misguided deal with the Castro regime."