The Government has said it has no information about any alleged payments.
There are about 20 people at the protest.
Amnesty International executive director Grant Bayldon will be attempting to hand over the controversial report when the Australian Consulate opens.
He said it was important for New Zealand to stand up for human rights.
"Australia is New Zealand's nearest neighbour. As a country that respects human rights...if we don't speak out, who will?"
The peaceful protest includes a range of Amnesty International members and the gathering is getting toots from passing commuters.
Mr Bayldon said the New Zealand Goverment needed to speak up.
He said the report included serious evidence of trans-national crimes being committed by Australian officials.
"So far we've had a very vaguely worded statement from Prime Minister [John Key] that he personally didn't know anything about it. We need something much more thorough than that.
"The response from the Australian Government yesterday to very serious claims has just been political bluster... nothing substantive."
Mr Bayldon then attempted to take the report inside but was asked to wait outside. The supporters have now formed a wall facing the Consulate doors.
Amnesty International is calling for a Royal Commission of Inquiry into the allegations.
"We do need to know from the New Zealand Government just what they know about the activities," Mr Bayldon said.
"We need the New Zealand Government to speak publicly and strongly.
"The aim of the protest was to deliver the report to the Australian Consul - and ask him to raise the concerns with the Australian Government, Mr Bayldon said.
As security guard arrived to escort Mr Bayldon up to the consulate, cheers erupted from the waiting supporters.
Mr Bayldon returned from handing the paper to a consulate official and said he had been assured the concerns would be passed to the Consul.
It was now a waiting game, he said.
"Really what we need to see now is the Australian Government take the evidence in that report seriously.
"We'll also be monitoring Australian Government activities off it's northern coast to see if any other cases like this appear."