At least 10 people have been killed in the worst unrest to hit Papua in years, as thousands have taken part in anti-racism rallies.
Human Rights Watch's Australia Director, Elaine Pearson, says the deaths need to be investigated, including a bloody clash in Deiyai regency.
Indonesian police said at least five people and a soldier were killed in Deiyai when security forces were attacked during a riot on August 28.
A former Deiyai resident, John Pakage, said he and hundreds of others have fled the regency.
"The situation in Deiyai until now [is] tense. And then many military Indonesians come to West Papua, also Deiyai and many violence."
John Pakage said eight civilians were killed in Deiyai when soldiers opened fire on what he says was a peaceful demonstration. The claims are consistent with how the incident has been described by rights groups and activists.
A government-imposed internet blackout across Papua which has only been gradually lifted has made verifying information difficult.
A police spokesperson, Ahmad Mustofa Kamal, was quoted by local media as saying 14 people have been named suspects in connection with the Deiyai riot for crimes including unlawfully possessing firearms, opposing authorities and incitement.
News outlet Suara Papua reported on Thursday the West Papuan suspects are still undergoing treatment at a local hospital after they were injured in the clash.
In its statement on Saturday, Human Rights Watch said Indonesia should also investigate an alleged incident in Jayapura on September 1 when a vigilante mob, along with police and soldiers, stabbed a Papuan student to death and injured more than 20.
A video taken in Fakfak - where nationalist civilian militia groups have clashed with Papuan protestors - showing a disembowelled Papuan man should also be investigated, it added.
"Governments concerned about the unrest and violence in Papua should press the Indonesian government to take prompt action to end the bloodshed, protect the rights of all, and allow full and open reporting of the situation," Ms Pearson said.