Six asylum seeker boat crew members have told Indonesian authorities they were each given $US5000 by Australian officials to return to Indonesia.
The federal Labor opposition has asked the auditor-general to investigate the claims, while Indonesian authorities have launched their own investigation and sought an explanation from the Australian ambassador Paul Grigson.
International law experts have suggested the payments are tantamount to the Australian government funding people-smuggling.
Prime Minister Tony Abbott has refused to confirm or deny the payments were made, saying only that stopping the boats was good for Australia and Indonesia.
Scott Morrison, who initiated Operation Sovereign Borders after the 2013 federal election, said the operation was being conducted lawfully.
"I have every confidence that officers working as part of Operation Sovereign Borders, based on my own experience of them, ... have always and will always operate lawfully," he told reporters in Canberra on Monday.
The government's policy was "if a boat leaves Indonesia, it's going back".
Parliamentary secretary Alan Tudge said the allegation was "unfounded".
Labor immigration spokesman Richard Marles has written to the auditor-general seeking an inquiry.
"If this happened, there are serious questions about the legal basis upon which it has happened," he said.
Independent senator Glenn Lazarus wants the government to resign if the allegations are found to be true.
Foreign Minister Julie Bishop appeared to rebuke Indonesia over its request to Mr Grigson to provide information about the alleged payments.
The best way for Indonesia to resolve its concerns about Australia's operations to stop asylum-seeker boats was to enforce sovereignty over its borders, she told The Australian.
International law expert Don Rothwell says any payment was tantamount to people smuggling, but he doubted Indonesia would take any action against Australia.
The Greens will ask the Australian Federal Police to investigate the claims and establish whether any laws have been broken.
They will also seek the tabling in the Senate of any documents relating to the payment.
"(Mr Abbott) doesn't have a mandate to break the law and he doesn't have a mandate for handing out big wads of cash out on the ocean," Greens immigration spokeswoman Sarah Hanson-Young told reporters.
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