Brigadier General Gusti Putu Danny, the head of Papua's Intelligence Agency was shot near Dambet Village in the Puncak District on Sunday.
The Indonesia's president has ordered a crackdown on what he calls armed criminal groups.
The Indonesian media has also reported the chairman of the People's Consultative Assembly in Papua, Bambang Soesatyo, urging the government to deploy forces at full strength to crush the Papuan rebellion.
He is quoted saying "destroy them first. We will discuss human rights matters later."
The Australian West Papua Association's Joe Collins says these sorts of statements have the potential to cause an escalation of violence, leading to the security forces conducting military sweeps in the area.
He said "we all know what happens when the Indonesian military undertake security operations, houses get burnt, livestock gets killed, gardens destroyed and people literally flee into the jungle where they face starvation".
Collins said instead Widodo should order his military to return to barracks as a way of easing tensions.
Photo AFP/RNZ Pacific CInaption: Indonesian President Joko Widodo