Labor says the government must come clean on allegations Australian officials paid-off people smugglers, in order to restore fractured relations with Indonesia.
The scandal over the boat payments took another twist on Saturday, with revelations Indonesian police accepted bribes from the same people smugglers.
The Weekend Australian reported police were paid to allow the departure of a boat to New Zealand, the crew of which were later given US$30,000 by navy officials to return to Indonesia.
The report says the Australians were certain the boat was unseaworthy, and they were concerned people could end up in the water.
Opposition foreign affairs spokeswoman Tanya Plibersek said Prime Minister Tony Abbott owed a full explanation of Australia's involvement in the scandal.
"We have seen the foreign minister and the immigration minister flat out deny it and then the prime minister seems to indicate that this may have happened," she said in Sydney.
"It is absolutely vital that the prime minister does what he has to do to get this relationship back on track."
Mr Abbott skirted the allegations at a Sydney Liberal Party function on Saturday.
He instead made a dig at opposition leader Bill Shorten, and claims the former Labor government had also paid-off people smugglers.
"On Monday, Mr Shorten attacked us for allegedly doing something to turn around boats, which it turned out he tried to do exactly the same - only it didn't work when he tried to do it," Mr Abbott said.
Indonesia's foreign affairs ministry claims to have evidence Australian officials paid the crew to turn their boat around, and has demanded an explanation from Australia.
Indonesian vice-president Jusuf Kalla has said the payments would amount to bribery and possibly even people-trafficking.
In other developments, Australia's top medical organisations have called for urgent amendments to the Border Force Act, so they can freely speak about the healthcare problems detainees face at immigration centres.
They have released a joint statement, saying it is "inconceivable" they could face up to two years' jail for sharing information about conditions at the centres.
-AAP