The New Zealand-based Indonesia Human Rights Committee has called on the government to act on the release of a video showing Papuans being tortured in Indonesia.
Indonesia's military chief says an investigation will deal with the video which implicated the security forces.
The Committee says the New Zealand government must pursue answers about the human rights abuses.
It says this is no time for New Zealand to offer police training programmes to Indonesia and they should be ended.
Human rights organisations have highlighted the continued abuses in Papua where Indonesia has been fighting a low-level insurgency ever since it seized the territory more than 40 years ago.
Meanwhile in Jakarta, the New Zealand foreign minister, Murray McCully, and his Indonesian counterpart, Marty Natelagawa, have launched the Indonesia-New Zealand Friendship Council.
Mr McCully says Indonesia is a crucial relationship for New Zealand both bilaterally and as a leader within ASEAN.
He also says it's New Zealand's eighth largest trading partner.