West Papua Action Auckland is urging the government to do more to protect people from ongoing security force violence in Indonesia's Papua region.
Spokesperson Maire Leadbeater said Indonesia was reponsible for decades of human rights abuses and the West Papuan people wanted self-determination.
She said New Zealand was a regional leader and was failing to take a stand against what was happening to its Pacific neighbours.
"We're on the Security Council, we've got high international profile and to some extent we are seen as a country with an independent foreign policy," she said.
"We have these opportunities that we seem to just let slip in favour of quiet diplomacy and good relations with Indonesia."
Ms Leadbeater said New Zealand should sever all military ties with Indonesia.
"Our military ties with Indonesia are not great. They are very small so it wouldn't be a huge issue really, just to cut them off altogether as a strong statement of our disapproval for the ongoing abuses committed by the Indonesian military and their failure to call to account those responsible for decades of documented human rights abuses against the West Papuan people."
The West Papua situation made international headlines in mid-December when Indonesian authorities opened fire on a peaceful protest in Papua's Paniai, killing five school students and injuring 20 others.
Ms Leadbeater said there must be an independent investigation into those events.
"The government should be openly, in a megaphone kind of way, calling for a truly independent investigation of the events that took place in Paniai. That's the kind of thing I would like to see them do much more strongly."