Havana (CNN)A day after making a historic arrival in Cuba, U.S. President Barack Obama and Cuban President Raul Castro expressed hope that reforms would finally arrive to the island, despite the persistent grievances on both sides.

In an extraordinary sign of the shifting attitudes, both leaders took questions from reporters following prepared statements, a rarity in a country where media remains under strict state control.

“We have decades of profound differences,” Obama said when asked by CNN’s Jim Acosta what his message on human rights was during his “frank conversation” on the issue with Castro. “I told President Castro that we are moving forward and not looking backwards.”

“We will continue to stand up for basic principles that we believe in,” Obama said. “America believes in democracy. We believe that freedom of speech, freedom of assembly, are not just American values but universal values.”

Obama was speaking following an hours-long meeting with Castro at the Palace of the Revolution in Old Havana. Castro, making a statement after the session, acknowledged the “profound differences” with the United States on human rights.

But he also underscored areas where he argued that the U.S. was failing.

“We find it inconceivable that a government does not defend and ensure the right to health care,” he said.

He also said that he opposed “political manipulation and double standards in the approach to human rights.”

Obama met with Castro on his first full day in Cuba as part of his efforts to elicit change on the island. But even as he works to open economic channels here, a longstanding trade embargo prevents a full restoration of ties.

“Much more could be done if the U.S. blockade could be lifted,” Castro said in a statement following his meeting with Obama at the Palace of the Revolution in Old Havana. “The most recent measures adopted by his administration are positive but insufficient.”

Castro also insisted upon the return of the Guantanamo Bay Naval Station to Cuba during his remarks, which were translated from Spanish.

Earlier, Obama and Castro shook hands before their sit-down, the third time the pair have met for bilateral talks since the resumption of diplomatic relations in 2014. It was unclear whether the leaders would later take questions from the press.

Obama started his morning laying a wreath by the Jose Marti memorial, a massive monument to the Cuban revolutionary leader where a Cuban military band played the “Star Spangled Banner,” another in a series of previously unthinkable moments that marks this week’s visit.

The sight of a sitting American president setting foot on the island was a novelty for most Cubans. The last U.S. leader to visit was Calvin Coolidge, who voyaged into Havana Harbor on a battleship in 1928.

He also told Castro he had a “great” dinner at a “paladar” — one of hundreds of privately run restaurants that only recently became permissible in the state-run economy. Those types of businesses, along with new investments from American firms, give U.S. officials hope that Cuba is on a path to open its economy after decades of isolation.

READ: How Cuba has changed between presidential visits

The meeting provides Obama and his aides another reality check on their mission to extract reforms from Castro. Until this point, there have been few signs that the government here is willing to work as quickly as the Obama administration hoped in opening the state-run economy and improving human rights.

“Change is going to happen here and I think that Raul Castro understands that,” Obama said in an interview with ABC News taped Sunday night.

“Our intention has been to get the ball rolling, knowing that change wasn’t going to happen overnight,” Obama said. “Although we still have significant differences around human rights and individual liberties inside of Cuba, we felt that coming now would maximize our ability to prompt more change.”