The Labour Party is calling on Prime Minister John Key to seek an assurance from Australia it does not pay people-smugglers to turn their boats around.
Migrants trying to reach New Zealand said crew on their vessel, intercepted by an Australian patrol in May, were paid to turn back to Indonesia.
Senior Australian government ministers, including Prime Minister Tony Abbott, are refusing to confirm or deny the claims.
Prime Minister John Key said he had no knowledge of whether Australian officials paid people-smugglers to turn around a boat full of refugees.
But Labour leader Andrew Little said under no circumstances should money be given to people-smugglers.
"The least that John Key should be doing is seeking information from Tony Abbott straight away and an assurance that this isn't happening and, that if it is, that it's stopped immediately and that they are dealing with the issue of people-smuggling in a way that the international community would accept," Mr Little said.
Mr Key told Morning Report he had seen the reports alleging a payment was made but had not been advised that New Zealand was involved or knew about it.
He said New Zealand authorities would have been talking to their Australian counterparts, but that would have been about the boat's movements.
"All I was advised of is that there was a boat that was coming, the belief that it had both the capability in terms of the boat itself, and the crewmanship of the sailors was estimated to be good enough for them to potentially do it. So it was all around the logisitics of the boat, but nothing else."
Mr Key was asked what he thought about paying people-smugglers to take their boats back.
"I can sort of see the arguments both ways. On the one had they are issues, in terms of a flood of boats, you don't want that happening.
"I think the counter-argument of course would be a pretty simple one, which would simply be my view, and I think most people's view, of boat smugglers, is a very poor one - these people that prey on people that are in a very difficult position."
Meanwhile, Immigration New Zealand said a police officer from this country is an observer in the Indonesian police-led investigation into the alleged people-smuggling operation.
In a statement, a spokesperson said the investigation was supported by the Australian Federal Police, but would not give any further details for operational reasons.
The boat with 65 people on board was intercepted by an Australian border patrol after setting off from West Java on 5 May. The asylum seekers told police the Australians transferred them to a more seaworthy boat and escorted them back to Indonesian waters.
However the vessel crashed onto a reef near the remote Rote Island, off West Papua, in late May, where it was found by fishermen and rescued by the Indonesian navy.
One of the migrants told Radio New Zealand that when the boat was intercepted, maritime authorities spent several hours talking to the boat's captain and crew, after which the captain was seen putting Australian money into his pocket.
Speaking from Kupang, Indonesia, Nazmul Hassan, told Morning Reportat least $A7200 was paid to the captain and crew for each passenger. Mr Hassan said Indonesian authorities later confiscated much of that money.
A Sri Lankan asylum seeker called Kajuran told ABC News a similar story, and an Indonesian police official told Fairfax media he saw bundles of cash allegedly paid by Australian officials to the crew.
The United Nations refugee agency UNHCR interviewed all 65 passengers who said the crew received a payment from Australian authorities, spokesman James Lynch said.
Australian opposition calls for investigation
The Australian Green Party is accusing the Australian government of playing a cat and mouse game with the truth over whether payments were made.
Immigration spokesperson Sarah Hanson-Young told Morning Report her party was looking for support in the Senate for a bill to force the Government to come clean on the issue.
Australia's Labor Party is calling on the country's Auditor-General to investigate whether there were any government payments.