HAVANA — The 54-year economic embargo of Cuba needs to end, President Obama and Cuban President Raúl Castro said Monday, so the economic ties between the two nations can improve.

"The embargo's going to end," Obama said. "When, I can't be entirely sure. ... The reason is that what we did for 50 years did not serve our interests or the interests of the Cuban people."

"The list of things we can do administratively is growing shorter," said Obama, who said that "for more than half a century, the sight of a U.S. president here in Havana would have been unimaginable."

Castro said "much more could be done if the U.S. blockade were lifted." While there has been much progress since December 2014 in drawing the two countries closer together, he said, "there are profound differences between our countries that will not go away."

Both leaders said the major differences focused on human rights and political freedom. Obama said relations "will not be transformed overnight." He said the United States will continue to push for more democracy in Cuba and improved human rights.

"Please give me the name of a political prisoner, and we will release him," Castro said in the post-meeting news conference.

Obama repeatedly said that he welcomed criticism of the United States from Castro and other Cuban leaders, which he called a sign of progress and that the two nations can speak candidly.

Human rights, Obama said, does not have to be the only issue U.S. and Cuban leaders discuss in the future, "but this is something we're going to stay on."

Castro said he did not think human rights issues "should be politicized." Castro said human rights mean different things to different countries. For example, women in Cuba receive equal pay for the same work as men, which is not true in other nations.

During the news conference, Castro's aides stood behind a curtain and often whispered comments to him.

Obama and Castro's meeting Monday was their third face-to-face encounter since the two countries began to normalize relations 15 months ago, but it was the first on Castro's home turf and the first visit of a U.S. president to the island in 88 years.

Castro said while differences remain between the two countries, Obama's visit was a key part toward building a new and positive relationship with the United States. Ties between the two nations started to fray in early 1959, when Castro's brother, Fidel, took power after a revolution ousted the former dictator Fulgencio Batista.

The United States then backed an unsuccessful invasion by Cuban exiles in April 1961 and started the economic embargo in February 1962.

Obama said the leaders deepened agricultural ties with Cuba. "With only 90 miles between us, we are natural trading partners," Obama said. He echoed Castro's call for Congress to end the embargo.

The United States has problems with the human rights records of many nations, such as China, Obama said. Despite those disagreements, he said, economic ties can improve.

Before their meeting, Obama and Castro reviewed an honor guard at the Palace of the Revolution and listened to the national anthems of both countries. Their two back-to-back meetings were the most extensive high-level talks between the United States and Cuba in decades. The first was one-on-one, with only translators, security and perhaps a close aide in the room. Afterward, the meeting was expanded to include top diplomats in both delegations.

While the United States has agreed to allow direct flights to Cuba, the Cuban government needs to do more, said Sen. Amy Klobuchar, D-Minn., who is part of a bipartisan congressional delegation that traveled with Obama.

"There have been some baby steps taken when it comes to the economy and the release of dissidents. More has to happen on the Cuban side," Klobuchar said.

Obama and Castro have met twice before: first at the Pan-American summit in Panama and again at the United Nations General Assembly in New York. There have been no plans announced for Castro to visit Washington.

Obama began the day with a wreath laying at a memorial to Jose Marti, the turn-of-the-century Cuban nationalist leader considered a unifying figure in Cuban history.

"It is a great honor to pay tribute to Jose Marti, who gave his life for independence of his homeland," Obama wrote in the guest book at the Marti memorial."His passion for liberty, freedom, and self-determination lives on in the Cuban people today."

After the meeting with Castro, Obama will participate in an entrepreneurship summit hosted by broadcast journalist Soledad O’Brien. The Obama administration wants to boost the emerging cuentapropistas who are increasingly making a living independent of government-owned enterprises.