US President Barack Obama has urged Cuba to improve its record on democracy and human rights as his counterpart Raul Castro hit out at America’s “double standards”.

During an historic visit to the Communist island, Mr Obama said the two had “frank and candid” discussions about human rights as well as areas of cooperation.

Mr Castro said they could achieve much better relations if the US lifted its 54-year-old trade embargo on the island.

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“We continue to have serious differences, including on democracy and human rights,” Mr Obama said at a joint news conference, where Mr Castro made the rare step of taking questions from journalists.

In response to a question on political prisoners, Mr Castro angrily demanded to be shown a list of such detainees, reflecting Cuba’s position that it holds no such prisoners.

“Give me a list of those political prisoners right now and if the list exists they will be released before the night is through,” Mr Castro said.

The two leaders held face-to-face meetings a day after Mr Obama arrived for the first visit by a US president in almost 90 years.

The trip would for decades have been unthinkable but became possible after secret talks led to a 2014 agreement to normalise relations between the two Cold War-era foes.

The opening ended decades of US efforts to force Cuba to change through isolation.

But Mr Obama is under pressure from critics at home to push Mr Castro’s Communist government to allow political dissent and further open its Soviet-style economy.

Putting aside differences for ‘a new day’

The two leaders vowed to set aside their differences in pursuit of what the US President called a “new day” for the relationship between the neighbours.

Mr Castro said the former enemies should take inspiration from US endurance swimmer Diana Nyad, who in 2013 managed on her fifth attempt to become the first person to swim from Cuba to Florida without a shark cage.

“If she can do it, we can do it too,” Mr Castro told journalists after more than two hours of talks with Mr Obama in Havana’s Palace of the Revolution, the nerve centre of the communist government that has ruled Cuba since the takeover by Raul’s brother Fidel Castro in 1959.

Trying to draw a line under past heavy-handed US intervention in the island’s affairs, Mr Obama vowed that “Cuba’s destiny will not be decided by the United States or any other nation”.

But he insisted that Washington was not going to give up pressing for political freedoms in Cuba, where the Communist Party controls politics, the media and the economy.

The US “will continue to speak up on behalf of democracy,” he said.

Meeting Mr Castro for only the third time for formal talks, Mr Obama was greeted by a military band at the Palace of the Revolution.

Mr Obama, under pressure back home to show that his scrapping of more than half a century of US hostility to the Castro regime is paying off, then sat for discussions against a backdrop of tall tropical plants and the two countries’ flags.

Earlier, he laid a wreath at the monument of Cuban independence hero Jose Marti.

On Tuesday (AEST), he was to give an address carried live on Cuban state television, and then attend a baseball game between the national team and Major League Baseball’s Tampa Bay Rays, before flying out.