US President Barack Obama declared a "new day" between the United States and Cuba following talks with Cuban President Raul Castro at which the Cuban leader repeated his call for the end to the decades-long US trade embargo against the communist island nation.

"Much more could be done if the US blockade were lifted," Castro told reporters after the meeting, using the terminology Cuba prefers for the US policy that has prevented most trade between the neighbours for more than half a century.

Castro called recent moves by Obama's administration to improve relations "positive but insufficient" and again demanded an end to the embargo, which requires an act of Congress. He also called for the return of the US naval base at Guantanamo Bay, Cuba.

Obama has been able to make only "small adjustments" to the embargo, but predicted it would end eventually because the economic isolation had not worked in the US interest.

Despite a rapprochement between Washington and Havana that saw the resumption of diplomatic relations last year, major differences remain particularly over human rights and Cuba's treatment of political dissidents.

Obama said he raised human rights during his meeting with Castro, but had also heard criticism from the Cuban president on issues such as poverty and race relations in the United States.

Human rights and democracy will continue to be impediments to the strengthening of ties, he said.

"To the extent that we can have a good conversation about that and to actually make progress, that, I think, will allow us to see the full flowering of a relationship that is possible," Obama said. "In the absence of that, I think it will continue to be a very powerful irritant."

He noted the issue is not unique to Cuba and the US has stressed human rights concerns with other nations with which it has relations, including China and Vietnam.

Obama called the discussions on human rights "fruitful," and stressed the US does not view Cuba as a threat even as it continues to stand up for basic human rights principles.

"Cuba's destiny will not be decided by the United States or any other nation," Obama said. "The future of Cuba will be decided by Cubans."

Castro responded testily to journalists' questions about human rights, denying the country has political prisoners.

"Give me a list of the political prisoners and I will release them immediately. Just mention the list. What political prisoners?" Castro demanded.

At the end of the press conference there was an awkward moment when Castro tried to raise Obama's arm overhead in an attempt to punctuate their newly formed bond. But he had to lower his arm clumsily when the US president did not reciprocate.

Castro formally welcomed Obama to Havana earlier Monday and the leaders reviewed a Cuban military honour guard at the Palace of the Revolution before sitting down for talks.

Obama, the first US president to visit Cuba in nearly 90 years, introduced Castro to Secretary of State John Kerry and other US diplomats and advisors on hand for the trip.

Decades of hostility between neighbours on opposite sides of the political spectrum have dissipated since Obama and Castro announced an agreement in late 2014 to end what effectively had become a stalemate in relations dating back decades.

Diplomatic ties were restored in July, and little by little other hindrances to cooperation have been dropped. Last week the United States loosened some travel restrictions on Cuba, including allowing US citizens to visit the country for "people-to-people" educational trips, and eased restrictions on banking services.

Direct postal services also recently restarted, eliminating the need for letters and parcels to be sent via third countries.

Obama's stay will not include a meeting with Castro's brother Fidel, the 89-year-old revolutionary who ruled the communist island for decades after the revolution. Fidel Castro has consistently expressed hostility toward the US, which implemented an embargo against Cuba in 1961.

Obama and first lady Michelle Obama attended a state dinner later Monday in the Palace of the Revolution where a Cuban orchestra entertained the guests. Castro and the Obamas were welcomed with applause in the room prepared for the dinner. Castro, a widower, attended the event unaccompanied.

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