WASHINGTON—The U.S. transferred 15 Guantanamo Bay detainees to the United Arab Emirates on Monday, the largest such movement yet in President Barack Obama’s push to remove most prisoners from the offshore prison before he leaves office in January.

The transfer of 12 Yemenis and three Afghans from the Cuba facility to the U.A.E. leaves 61 detainees, a significant drop from the 242 men imprisoned there in 2009 when Mr. Obama took office but short of the president’s longtime goal of closing the lockup.

The Obama administration has faced persistent resistance from Congress and the Pentagon to closing the prison.

Since its opening after the Sept. 11, 2001, terror attacks, the prison has held nearly 800 men. The Obama administration has released nearly 200 detainees, while 532 were released during the George W. Bush administration.

In recent months, the transfers have increasingly involved Mr. Obama, Secretary of State John Kerry and Vice President Joe Biden, who at times have worked to “close the deal” with foreign leaders on resettling or repatriating detainees, officials said.