Two migrants who were on a people-smuggling boat at the center of claims Australia's navy paid the crew to turn back to Indonesia say they saw the money handed over.

The allegation of payments to people smugglers has strained relations between Indonesia and Australia, which has a policy of turning back any migrants who arrive by boat.

One of the men in an interview with Indonesian television said: "It was not small money, everybody saw it."

Police in Indonesia's East Nusa Tenggara province reported that the captain and five crew members detained had about $30,000 in cash.

The group said they were paid to return the migrants to Indonesia after being intercepted by an Australian navy ship on May 20.

Australia's prime minister has sidestepped questions about the matter.