GENEVA — Asian migrants on a boat that was intercepted by the Australian authorities three weeks ago have told refugee workers that the Australians paid the smugglers to take them back to Indonesia, a United Nations official said on Friday.

The 65 migrants — including 54 from Sri Lanka, 10 from Bangladesh and one from Myanmar — gave their accounts to employees of the United Nations refugee agency in Indonesia, where they were brought ashore and placed in detention, said Babar Baloch, a spokesman for the agency in Geneva.

“They are telling us that they were intercepted by Australian officials at sea,” Mr. Baloch said in a telephone interview. “They were taken on board an Australian customs boat for four days. They were then put on two blue boats and the crews were paid to take them back to Indonesia.”

The migrants’ account has stoked debate over the hard-line policy on illegal immigrants that helped Prime Minister Tony Abbott of Australia win office in 2013 but exposed the nation to pointed criticism from United Nations agencies.