Former immigration minister Scott Morrison says he has "every confidence" Operation Sovereign Borders officers have acted lawfully, amid calls for investigations into claims bribes have been paid to people smugglers.

Crew members and asylum seekers from a vessel which ran aground on an Indonesian reef earlier this month have said Australian officials handed over thousands of dollars for the vessel to return to Indonesia.

Indonesia is investigating the claims and has asked Australia's ambassador in Jakarta for an explanation.

Mr Morrison was immigration minister from the Government's election until December last year, when he began in the social services portfolio.

He would not say whether payments happened during his time as minister, but said he was confident officials acted lawfully.

"I have every confidence that officers working as part of Operation Sovereign Borders, based on my own experience of them, is that they have always, and will always, operate lawfully," Mr Morrison said.

"We've delivered on what we said we'd do for the Australian people. Others can speculate on speculation and on allegations and things of that nature.

"The simple truth is if a boat leaves Indonesia, it's going back.

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"That's how this Government operates."

The Opposition's immigration spokesman Richard Marles has requested an urgent independent investigation into the claims.

"Last night I wrote [to] the auditor-general and have asked firstly for an investigation as to whether these bribes have been paid," Mr Marles said.

"If this happened, there are serious questions about the legal basis upon which it has happened."

What we know: People smuggler payment claims Indonesian police say an asylum seeker boat was intercepted by an Australian border patrol after setting off from West Java on May 5

Indonesian police say an asylum seeker boat was intercepted by an Australian border patrol after setting off from West Java on May 5 A boat ran aground on a reef near remote Rote Island, off West Timor, on June 1

A boat ran aground on a reef near remote Rote Island, off West Timor, on June 1 It was carrying 65 asylum seekers from Sri Lanka, Bangladesh and Myanmar, including four women and three toddlers

It was carrying 65 asylum seekers from Sri Lanka, Bangladesh and Myanmar, including four women and three toddlers The asylum seekers told Indonesian police Australians had intercepted them, transferred them onto a more seaworthy wooden boat, gave them dried fruit, biscuits, fuel and life jackets, and escorted them back to Indonesian waters

The asylum seekers told Indonesian police Australians had intercepted them, transferred them onto a more seaworthy wooden boat, gave them dried fruit, biscuits, fuel and life jackets, and escorted them back to Indonesian waters The six crew members told Indonesian authorities they were each given $US5,000 by Australian officials to sail back to Indonesia

The six crew members told Indonesian authorities they were each given $US5,000 by Australian officials to sail back to Indonesia The asylum seekers also told the UNHCR the crew were paid by Australian authorities

The letter asks, if payments have been made, whether it "would be a proper use of public resources".

"I ask you to consider investigating these concerning circumstances, including if any payment to people smugglers or their agents was made, and if so, the nature of how or whether it was properly authorised," it reads.

Meanwhile, Foreign Minister Julie Bishop has suggested Indonesia better secure its own borders.

"The best way for Indonesia to resolve any concerns it has about Operation Sovereign Borders is for Indonesia to enforce sovereignty over its borders," Ms Bishop told News Corp Australia.

"Operation Sovereign Borders is necessary because Indonesian boats with Indonesian crews are leaving Indonesia with the express intention of breaching our sovereignty, facilitated by illegal people-smuggling syndicates.

"I look forward to hearing the full results of Indonesia's investigation of the people smuggling crimes committed in Indonesia, including any breaches of passport and visa laws, and establishing whether the captains and crews of these boats are part of people-smuggling syndicates or are paid by them."

Taxpayers deserve to know how money spent: Xenophon

The Government was expected to be pushed in Parliament to explain if payment occurred.

Independent senator Nick Xenophon said he wanted to know if the allegations were true.

"Taxpayers' money is at stake," he said.

"We deserve to know how it was spent, whether taxpayers' money was used or not and the rationale for that."

Greens senator Sarah Hanson-Young said the party would try to use the Senate to demand the release of documents to show if payments were made.

"The Greens will also be referring the matter for investigation to the AFP," she said.

"The Indonesian police can investigate this matter, so too can the Australian Federal Police.

"The Prime Minister says he's got a mandate to stop the boats.

"Well, he 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."

Prime Minister Tony Abbott responded to questions about the allegations by focusing on his Government's record.

"There's really only one thing to say here and that is that we have stopped the boats," Mr Abbott said on Sunday.

"That's good for Australia, it's good for Indonesia."

Labor is also pressuring Immigration Minister Peter Dutton.

Last week he said no money had been paid but on Sunday he reverted to saying the Government would not comment on operational matters.

"In the course of last week he categorically ruled out, he staked his reputation, that no people smugglers have been paid taxpayer money in the carrying out of the people smuggling," Opposition Leader Bill Shorten said.

"Yet today, the Minister for Immigration has refused to stand by his earlier categorical denials."