The Vatican secretary of state, Cardinal Pietro Parolin, made the request during a Vatican meeting with US Secretary of State John Kerry.
Vatican spokesman Rev. Federico Lombardi said the two sides discussed the US commitment to closing the facility.
He said Parolin expressed the Holy See's desire that "favorable attention be paid to finding adequate humanitarian solutions for current inmates."
Just this past weekend, he sent a letter of Christmas greetings to inmates at a prison in Latina, urging them to use their time in detention for personal and spiritual growth.
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Without citing the US by name, Francis has also harshly criticized extraordinary renditions, which the CIA used after the Sept. 11 attacks to take terror suspects to third countries for interrogation, and often torture.
He has also denounced life prison terms as a "hidden death penalty," and said putting inmates in isolation was a form of "physical and psychological torture."
A senior US State Department official, who wasn't authorized to speak publicly about the matter and demanded anonymity, said Kerry "described recent progress in our diplomatic efforts to transfer detainees to third countries, including to Uruguay.