On Monday, US President Barack Obama said he and Cuba's Raul Castro had "frank and candid" discussions about human rights, as well as areas of cooperation.

"We continue to have serious differences, including on democracy and human rights," Obama said at a joint news conference after their meeting. He said rights remained an impediment to the strengthening of ties. A "full flowering" of the relationship could only happen with progress on the issue of rights.

"In the absence of that, I think it will continue to be a very powerful irritant," Obama said at the news conference, which was broadcast live on Cuban state television.

Obama has become the first sitting US president to visit the Caribbean island since 1928. Speaking in Spanish, Obama hailed a "nuevo dia," or new day, in relations between the former Cold War foes. Since 2014 there have been talks between the two countries, some of them facilitated by the Vatican.

In Havana's Palace of the Revolution, Obama vowed that "Cuba's destiny will not be decided by the United States or any other nation."

Obama said the US "will continue to speak up on behalf of democracy."

Earlier in the day, Obama laid a wreath at the memorial to the 19th-century poet, writer and independence hero Jose Marti. He wrote in the guest book: "It is a great honor to pay tribute to Jose Marti, who gave his life for independence of his homeland. His passion for liberty, freedom and self-determination lives on in the Cuban people today."

Differences

It was the third meeting between the two presidents. Castro acknowledged that there were still "profound" differences over human rights and the decades-old US economic embargo. He pointedly refused to acknowledge that Cuba holds political 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," Castro said.

Castro said that the two countries could achieve much better ties if the US lifted its 54-year trade embargo on the island and handed back the Guantanamo Bay base to Cuba.

On a lighter note, the Cuban president said the former enemies should be inspired by the 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," Castro said.

The sporting theme continues on Tuesday, with a baseball match between the Cuban national team and visiting Tampa Bay Rays from Florida, which the presidents plan to attend.