The comments by Bruno Rodriguez Parrilla to the UN Human Rights Council in Geneva came a day after US President Barack Obama vowed again to shut the military prison, saying it was damaging US interests.
"We are deeply concerned about the legal limbo that supports the permanent and atrocious violation of human rights at the illegal naval base in Guantanamo, a Cuba territory that was usurped by the United States, a centre of torture and deaths of prisoners who are under custody," Parrilla said during a review of Cuba's own rights record.
"That prison and military base should be shut down and that territory should be returned to Cuba," he said.
The hunger strike, now into its 12th week, has heightened the pressure on Washington to shut what Obama has called a legal "no man's land".
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Obama said yesterday he did not want any inmates to die and urged Congress to help him find a long-term solution that would allow for prosecuting terror suspects while shutting down Guantanamo.
Even before the creation of the jail, the US Navy base was a source of dispute between Havana's communist rulers and bitter rival Washington.
The United States signed a long-term lease for Guantanamo Bay after helping Cuba throw off Spanish colonial rule at the end of the 19th century.
Already strategic for Washington's Caribbean regional policy because of its location in southeastern Cuba, it acquired additional importance during the Cold War after the 1959 Cuban revolution.