Obama: 'This Is A New Day — Es Un Nuevo Dia — Between Our Two Countries'

"This is a new day — es un nuevo dia — between our two countries," President Obama said after meeting with Cuban President Raúl Castro in Havana.

The two leaders agreed that there are still deep fissures between the two countries and that a healthy relationship between them will take work.

That uneasiness was apparent as soon as journalists began asking questions. Obama and Castro were not supposed to take questions, but a last minute change made that possible and Obama called first on CNN's Jim Acosta, who is Cuban-American.

In Spanish, Acosta asked Castro why his country kept political prisoners.

Clearly miffed, Castro asked Acosta to hand over a list of political prisoners.

"Give me a list after this press conference. If there are political prisoners, they will be released by nightfall. That's it," Castro said.

Almost immediately, The Center for a Free Cuba, which advocates for human rights on the island, sent over a list documenting more than 1,000 cases of persons who they say were "arbitrarily detained" for political reasons.

"The list is never complete," Frank Calzon, the nonprofit's executive director, said in a statement. "When President Obama announced back in December 17, 2014 that 50 some prisoners were to be released, we later discovered that some were re-imprisoned later."

The Cuban American National Foundation released its own list of 47 people the organization says are political prisoners.

Obama was diplomatic when he addressed Cuba's human rights record. He said the U.S. would continue to press the issue of freedom of speech and expression, much like it does around the world.

The United States, however, cannot force change on the island, he said.

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

Castro said it was unfair to focus solely on the issue of freedom expression. Cuba, he said, views many things as human rights, including the right to free healthcare and education.

"Here in Cuba, all children are born in a hospital, no matter what mountain they live on," Castro said. "In Cuba, men and women who do the same job earn the same."

All countries, he said, have failings on human rights but all countries also excel in other areas.

"We're going to work together so we can all achieve all of the human rights," Castro said.

Obama's official visit to Cuba began on Monday with a wreath-laying ceremony at the foot of a memorial to Cuban independence hero and poet José Martí.

It's worth pausing on that for a minute. The statue of Martí is also at the center of La Plaza de la Revolución, a square as important and revered in Cuba as Moscow's Red Square or Beijing's Tiananmen Square. On the other side, in the distance, the buildings for the ministries of defense and interior are framed with outline portraits of Ernesto "Che" Guevara and Camilo Cienfuegos, two of the country's bearded revolutionary heroes.

Fidel Castro used to give lengthy speeches at the square to huge crowds and often denounced U.S. imperialism.

Today, Obama stood solemnly before the statue of Martí as a Cuban military band played "The Star-Spangled Banner."

A few minutes later, and for the first time in almost 90 years, a Cuban president welcomed an American president.

Castro shook Obama's hand at the Palace of the Revolution in Havana, making history and bringing a symbolic end to one of the last rivalries of the Cold War. The two leaders met for a couple of hours and then they emerged to face the press.

Castro called on the United States to put Guantánamo back in Cuban hands and end the embargo. "The blockade is the single biggest obstacle to our economic development," Castro said.

Obama said that the embargo will end.

"The path we're on will continue beyond this administration," Obama said. "The reason is logic." Decades of isolation, he said, have not worked so it's time to try something new.

Castro said the story of Diana Nyad, who on her fifth try swam from Cuba to Florida without using a shark cage, should serve as an allegory for the two countries.

"If she can do it, we can do it," Castro said.

Obama returned to that metaphor toward the end of his remarks, saying, "The road ahead will not be easy. Fortunately, we don't have to swim with sharks."

In the evening, Obama will attend a state dinner at the Palace of the Revolution.