The UN Refugee Agency says it is trying to "corroborate" the individual accounts of asylum seekers who claim to have been abused by the Australian Navy as their boat was turned back to Indonesia.

Footage obtained by ABC News shows asylum seekers with severe burns to their hands, but it is impossible to verify how they received them.

Some of the asylum seekers who were turned back to Indonesia say they were abused and suffered burns after being forced to touch the boat's engine.

Indonesian police have indicated they do not have the power to investigate the allegations, and they want the United Nations High Commission for Refugees (UNHCR) to investigate.

"UNHCR has heard serious allegations of boats carrying potential asylum seekers being pushed back from Australia to Indonesia and of mistreatment during the process," a refugee agency spokeswoman in Jakarta told AFP.

"We are corroborating these individual accounts. If confirmed, we hope that the Australian authorities will conduct a swift investigation into these allegations."

A UN spokeswoman told the ABC that its inquiries did not qualify as an investigation, but the refugee agency was "asking additional questions to corroborate the facts".

"These are serious allegations and we need to be fairly sure before taking further action," she said.

Indonesian police say so far the only witnesses are the asylum seekers.

National Police spokesman Ronny Sompie says it cannot be determined whether the alleged mistreatment happened inside Indonesian waters.

Immigration Minister Scott Morrison has emphatically rejected the asylum seekers' claims.

The Federal Government has said it is willing to provide any documents and videos it has in order to refute the accusations.

The UNHCR has previously warned that turning boats back to Indonesia may be in breach of international law.

ABC/AFP