Mr Castro said more needed to be done to lift the US embargo on trade with Cuba and that the Guantanamo Bay detention camp must close.
Mr Obama, the first sitting president to visit Cuba since 1959, said the trade embargo would be fully lifted.
Mr Castro took questions from reporters – a rarity for him.
“Cuba’s destiny will not be decided by the United States or any other nation… The future of Cuba will be decided by Cubans not by anybody else,” Mr Obama said.
Asked about political prisoners in Cuba, Mr Castro denied it, telling journalists to “give him a list” and then they would be released “tonight”.
He also defended Cuba’s record on human rights and pointed to problems in the US.
“We defend human rights, in our view civil, political, economic, social and cultural rights are indivisible, inter-dependent and universal,” Mr Castro said.
Mr Castro is not usually subject to any aggressive questioning from reporters and called the prisoners question “not polite”, later ending the news conference by saying “I think this is enough”.
“Actually we find it inconceivable that a government does not defend and ensure the right to healthcare, education, social security, food provision and development,” he said.
President Obama and his aides hoped that the Cuban president, Raul Castro, would approach the news conference with an open mind.
The White House officials also hoped that Mr Castro would be receptive to new ideas and to new ways of doing things. Specifically, the US officials hoped that he’d take questions from reporters. Surprisingly enough, he did, marking a departure from his past.
The two men joked around during the question-and-answer period, and they worked out some of their differences. When one of Mr Castro’s aides interrupted his boss during the conference, for example, Mr Obama looked annoyed. But he and Mr Castro moved on, talking about the future of Cuba.
In a similar way, Mr Obama and his aides hope they can overcome other issues, including difficult ones such as human rights, as they forge a new relationship between the two countries.
Mr Obama could not say exactly when the trade embargo would be lifted, but recognised it was necessary.
“The reason is what we did for 50 years did not serve our interests or the interests of the Cuban people,” he said.
His administration has done what it can on lifting trade restrictions, he said, but further action will require Congress which is “not as productive in an election year”.
He also said further easing of the trade embargo will depend on actions Cuba takes on human rights.
