Indonesian Defence Minister Juwono Sudarsono concedes rogue elements from the country's security forces could be involved in the violence.
There has been trouble on the road to the province's Freeport mine since the weekend.
National police spokesman Nanan Soekarna told the Australian Broadcasting Corportation that of the five policemen hurt in new violence yesterday, two were shot and one is injured critically.
Workers home
Hundreds of workers from the Freeport mine have been ordered to stay at home rather than risk the long drive to work on the remote road.
Mr Grant, 29, was shot four times while travelling in a car on the Freeport road.