Havana: US President Barack Obama and Cuban President Raul Castro sparred over human rights issues, including the American prison at Guantanamo Bay and Cuba's political prisoners, media reports said on Tuesday. During a historic news conference on Monday evening in capital Havana, Obama and Castro acknowledged deep disagreements on these issues. But the two leaders also found common ground on the topic of the economic embargo on Cuba, which both want lifted. Obama went so far as to declare that "the embargo's going to end", though he did not say when, CNN reported. In an extraordinary sign of shifting attitudes, Castro was willing to answer one question on why his regime was keeping Cubans incarcerated for expressing anti-government views. "Did you ask if we had political prisoners? Give me a list of political prisoners and I will release them immediately," Castro said defensively. Unaccustomed to press conferences, Castro at first appeared confused at whether the question was directed to him and later asked for it to be repeated as he juggled the headphones he wore to hear its translation. Later, Castro delivered a litany of areas where he said the US was failing, from inadequate health care to lower pay for women. He ended the unprecedented question-and-answer session after a second inquiry on human rights, saying he had said "enough". In his own message on human rights, Obama defended his decision to come to Cuba even as government dissent is punished. "We have decades of profound differences," Obama said when asked 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". Obama and First Lady Michelle Obama were later welcomed at a state dinner, along with some members of US Congress and senior White House staff. The two leaders formally had an hour-long meeting earlier on Monday at the Palace of the Revolution in Old Havana, his third meeting with the Cuban leader since work began to reopen diplomatic ties to the island. After the meeting, Obama also participated in a business forum with Cuban entrepreneurs, US businessmen and representatives from Cuban state companies where he said he would continue working to adopt changes that would improve and increase access to internet on the island. Obama became the first president to visit Cuba after 88 years. He arrived on the island on Sunday. His three-day visit marks the culmination of a thaw in relations between Washington and the Communist island that began in December 2014 - 55 years after Fidel Castro seized power. The last and only American president to visit Cuba while in office was Calvin Coolidge in January 1928.