The land Guantanamo was built on was leased to the United States in 1903 and now Cuba want it back.
Obama has said he will not hand back Guantanamo Bay to Cuba after Cuban President Raul Castro made demands on the U.S. to hand it back.
BBC News reports:
US President Barack Obama “does believe that the prison at Guantanamo Bay should be closed down… but not the naval base”, the White House said.
The land on which the base stands was leased to the US by Cuba in 1903.
The Cuban government which came to power in the revolution of 1959 has long demanded its return, saying it is a violation of international law, but the US points to a legal provision making the lease permanent unless it is terminated by mutual agreement.
Last month the two countries announced a thaw in relations, agreeing to restore diplomatic ties severed in 1961. Delegations have begun negotiating the re-establishment of embassies.
However in a speech on Wednesday, Mr Castro said: “The re-establishment of diplomatic relations is the start of a process of normalising bilateral relations.
“But this will not be possible while the blockade still exists, while they don’t give back the territory illegally occupied by the Guantanamo naval base.”
This condition was rejected by White House spokesman Josh Earnest in remarks to the media on Thursday.
He agreed that President Obama was seeking to shut the prison at Guantanamo Bay, as it “only serves as a recruiting tool for al-Qaeda and other extremist organisations”.
“But the naval base is not something that we believe should be closed,” he said.