In the joint news conference, Obama and Castro clashed on the issue of human rights in Cuba, with the Cuban leader denying knowledge of any political prisoners in the island nation.
"What political prisoners? Give me a name, or names, or 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," Castro said.
President Obama's exclusive sit-down interview with David Muir will air tonight on "World News Tonight With David Muir" at 6:30 p.m. ET and on "Nightline" at 12:35 a.m.
Obama told Muir that while he had not given Castro a list today, the U.S. had given the Cuban president lists "in the past."
"They have responded intermittently to our engagement," Obama said. "And, and this, I think, is an example of why it was my belief that this would be a more successful mechanism for us to advance the values that we care about than an embargo and silence and no communications."
Obama is in the midst of a two-day trip to the island nation that comes after the two countries reestablished a bilateral relationship in December 2014 following more than five decades of severed relations.
The trip marks the first time in nearly 90 years a sitting U.S. president has visited Cuba.