The Australia West Papua Association says rallies by independence supporters in Indonesia's Papuan region this week were peaceful and not attended by security forces.
July the 1st marks the day in 1971 when Papuan leaders proclaimed the region's independence from Jakarta.
The Antara News had reported Major General Christian Zebua saying Indonesian soldiers would shoot any independence supporters who attended.
A spokesperson for the AWPA, Joe Collins, says the rallies, at least two in Papua and one in Java, were small but significant.
"I think threats of intimidation did have an effect on the West Papuan people, some people decided to stay at home. So although they were small, it does not go unnoticed. The West Papuan people they really really do want self-determination and any chance they get they will raise the issue."
Joe Collins says the international media and community watching what was happening yesterday would have influenced the military to step back.