SYDNEY, Australia — Australian opposition lawmakers said Saturday that they would press Prime Minister Tony Abbott to reveal whether the government paid smugglers to turn a boat full of migrants back to Indonesia after intercepting it at sea.

Migrants from the boat gave that account to workers for a United Nations refugee agency in Indonesia, a United Nations official said Friday. In an Australian radio interview that day, Mr. Abbott, asked about news reports that made the same assertion, neither confirmed nor denied it, but he said the government was determined to “stop the boats by hook or by crook.”

Richard Marles, the opposition Labor Party’s spokesman for immigration, said Saturday that Mr. Abbott’s refusal to clearly deny having paid human traffickers “leaves one with the only possible assumption that that may well have been exactly what happened.”

The minority Greens Party said it would submit a motion in the Senate, possibly as early as Monday, demanding that the government produce any documents related to the interception of the boat.