WASHINGTON (Reuters) - Two inmates from the U.S. military prison at Guantanamo Bay were transferred to Serbia on Monday as the Obama administration pressed ahead with its long-held goal of shutting the widely condemned facility at the U.S. naval base in Cuba.

The transfer of Yemeni national Mansur Ahmad Saad al-Dayfi and Tajik national Muhammadi Davlatov to Serbia reduced the number of detainees at Guantanamo to 76, with 27 of those approved for transfer once an appropriate country can be found, U.S. officials said.

"The United States appreciates the generous assistance of Serbia as the United States continues its efforts to close the Guantanamo Bay detention facility," Secretary of State John Kerry said in a statement, calling it a "significant humanitarian gesture."

It was the first time the United States has transferred Guantanamo Bay prisoners to Serbia, a Pentagon spokesman said.

After meeting Serbia's Prime Minister-designate Aleksandar Vucic in Belgrade, Victoria Nuland, the U.S. Assistant Secretary of State for European and Eurasian Affairs, said the Obama administration was grateful to Serbia for taking the two inmates.

Vucic said Serbia acted in line with good cooperation it has with the United States.

"Other countries took over (inmates), Germany took them, it was natural (for us) to do that ... I think this speaks well about our country and that this is a good signal for the future," Vucic said.

The transfers came just a day after another Yemeni national, Fayiz Ahmad Yahia Suleiman, was transferred to Italy.

Davlatov, 37, also known as Umar Hamzayevich Abdulayev, was approved for transfer nearly six years ago by six U.S. government departments and agencies.

Al-Dayfi, 37, also known as Abdul Rahman Ahmed, was approved for transfer in October by a review board that determined his detention was no longer necessary for national security, the Defense Department said in a statement.

The Obama administration had notified Congress of its intent to transfer the two men, as required by law, a State Department official said on condition of anonymity.

President Barack Obama had hoped to close the prison during his first year in office in 2009 but has faced opposition from many Republican lawmakers as well as some fellow Democrats.

Most of the inmates remaining at the prison have been held without charge or trial since being detained following the Sept. 11, 2001, attacks on the United States.

Al-Dayfi traveled to Afghanistan in mid-2001, trained at an al Qaeda training camp and was wounded by a coalition air strike, according to a U.S. military profile last year.

While a secret 2008 military assessment made public by the WikiLeaks anti-secrecy group portrayed al-Dayfi as a high-threat al Qaeda member, the military profile released last year said he probably exaggerated his involvement with al Qaeda. No al Qaeda leaders have identified him as a member, it said.

Davlatov was a member of the Islamic Movement of Tajikistan who was thought to have received training at an al Qaeda camp, according to a 2008 secret assessment by a military task force made public by WikiLeaks.

(Reporting by Lesley Wroughton and David Alexander; additional reporting by Aleksandar Vasovic in Belgrade; Writing by Doina Chiacu; Editing by Ralph Boulton)