"As we have previously stated we were not involved in dealing with the boat in May, and we have no information about any alleged payments."
Labour's foreign affairs spokesman David Shearer said that response was not good enough, and Mr Key needed to state that the New Zealand Government knew nothing, and was in no way implicated, about the apparent payments to people-smugglers.
"Two years ago John Key agreed to take 150 'boat people' for Australia in return for Australia intercepting any large influx of refugees suspected of being en route to New Zealand.
"Paying off people smugglers to turn back boats is wrong and is no way to address the issue.
"Our government should be making how we feel crystal clear to our neighbours across the ditch, as well as reassuring Kiwis it has had no involvement in any of this."
Mr Key has previously said he only found out about the payment allegations through media reports, and had no comment on the matter.
The Amnesty report, By Hook or By Crook, outlines evidence that Australian officials working as part of Operation Sovereign Borders paid six crew who had been transporting 65 people seeking asylum US$32,000 in crisp $100 bills.
The Australians also provided maps showing the crew where to land in Indonesia, the report states. Indonesian police showed an Amnesty researcher money confiscated from the boat's crew, which was all in new US$100 bills.
After it was turned around by Australian border patrol, the boat crashed onto a reef on Landu Island, a remote island near Rote.
The Amnesty investigation also found evidence that Australian officials may have paid money to another boat crew that was turned back in July.
"All of the available evidence points to Australian officials having committed a transnational crime by, in effect, directing a people-smuggling operation, paying a boat crew and then instructing them on exactly what to do and where to land in Indonesia," said Anna Shea, refugee researcher at Amnesty International.
"People-smuggling is a crime usually associated with private individuals, not governments - but here we have strong evidence that Australian officials are not just involved, but directing operations."
The turnback of the boat In May is the subject of an Australian Senate inquiry, which is due to report back in January. Officials have submitted that the boat was observed in poor and deteriorating weather conditions.
Green Party human rights spokeswoman Catherine Delahunty said the Amnesty report came after other Australian human rights breaches, including the treatment of hundreds of Kiwis detained in centres including on Christmas Island, before their deportation to New Zealand.
"It's time for the National Government to take a stand and say New Zealand won't support a country that has been cited 143 times for breaches of human rights," Ms Delahunty said.
"It may be awkward for John Key to take a stand against Australia but this is the kind of leadership he signed up for when he sought a seat on the United Nation's Security Council.
"John Key must rule out supporting Australia's bid for the Human Rights Council. We would also call on him to back Amnesty's call for a Royal Commission to investigate Australia's treatment of the asylum seekers," Ms Delahunty said.
