The promised new era in US-Cuban relations quickly gave way to old disagreements on Monday when Barack Obama and Raúl Castro clashed over human rights at an extraordinary press conference in Havana.

Hailing a “new day” between the two countries and predicting that the US economic “embargo will end”, Mr Obama met the Cuban president on Monday morning for the first formal engagement on a historic visit to Cuba that is the culmination of his dramatic announcement 15 months ago on restoring diplomatic relations.

However, the sharp disagreements over political values that have divided the two countries for decades swiftly resurfaced when a defensive Mr Castro denied that Cuba had any political prisoners and decried American “double standards” about human rights.

The visit by Mr Obama is a gamble by both sides — from the US that the presence of the president can help cajole Cuba to open its society and economy more quickly and from the Cuban regime that it can absorb US visitors and investment without loosening its tight political grip.

“Change is going to happen [in Cuba] and I think that Raúl Castro understands that,” Mr Obama said, shortly after arriving.

Until hours before the two leaders appeared before the media in the early afternoon, US officials did not know if they would answer questions or simply deliver statements, as the Cuban side initially demanded.

Once the press conference started, Mr Castro might have been forgiven for having second thoughts during a performance broadcast live on Cuban television that was at times prickly and uncertain. At one stage, an aide approached the platform to confer with the Cuban leader for some time while Mr Obama was speaking, leading the American president to say: “Excuse me.”

Asked by a member of the US press about political prisoners in Cuba, Mr Castro gave a defiant response. “Provide me the list. What political prisoners?” Mr Castro asked. “Give me a name or names, or when after this meeting is over, you can give me a list of political prisoners, and if we have those political prisoners they will be released before tonight ends.”

Mr Castro went on to defend a version of human rights that gives much more emphasis to healthcare access and education. “There are 61 international instruments recognised. How many countries in the world comply with them all?” he asked. “Cuba has complied with 47 of these human rights instruments. There are countries that may comply with more, there are those that comply with less.”

He also criticised the US for continuing to maintain a military base at Guantanamo Bay.

Human rights groups say that during Mr Castro’s presidency far fewer people have been imprisoned for long periods of time for their political views, but that there has been heavy use of short detentions. The local, dissident-run Cuban Commission for Human Rights and National Reconciliation estimates there were 2,555 such detentions in the first two months of this year.

Mr Obama, on the other hand, went out of his way to adopt a more conciliatory tone. “We had a very frank conversation around issues of democracy and human rights. Our starting point is we have two different systems, different systems of government, of economy. And we have decades of differences,” he says.

He added that “I personally don’t disagree with him” about the importance of education and healthcare. “It’s not for the United States to dictate to Cuba how they should govern themselves,” he added.

Cuban critics of the regime said the press conference had made Mr Castro look out of touch. “Castro behaves defensively and recalling the past. Obama looks quiet and looking into the future,” said blogger Yoani Sanchez on Twitter.

Speaking ahead of the visit, Richard Feinberg, a former White House official and Cuba expert, said the risk for the regime was that Mr Castro would be outshone by the US president. “You will have a youthful, vigorous mixed race leader who looks like the average Cuban and for the Cuban leadership that is an uncomfortable comparison with an ageing, distant leader.”

Ben Rhodes, deputy national security adviser, said the US regularly raises cases with the Cuban authorities, although they generally insist that the individuals have not been detained for political reasons. “I have shared many lists with the Cuban government,” he said.

After an evening of tourism in the old centre of Havana with his family on Sunday evening, including a visit to the city’s cathedral and dinner at a private restaurant, Mr Obama met Mr Castro on Monday morning at the Palacio de la Revolución and held a forum with Cuban and American business leaders in the afternoon. On Tuesday he will give a speech to the Cuban people, meet a group of dissidents and then attend a baseball game between the Tampa Bay Rays and the Cuban national team.

In an itinerary replete with heavy symbolism, Mr Obama laid a wreath at the memorial to Jose Marti, the Cuban independence leader. He was accompanied by Salvador Valdes Mesa, a member of the politburo of the Cuban communist party who took part in repelling the attack on the Bay of Pigs. In the background was a large image of revolutionary hero Che Guevara.

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