The new clash began at 05:10 Jakarta time (2210 GMT on Thursday) following provocation from one of the groups.
The groups, using traditional weapons, picked a new area to fight after the local police parked an armored vehicle on the street between the two warring neighborhoods on Wednesday.
The clashes have resulted in the death of one man and injuries to many more since the fighting began on Monday afternoon.
Police said the feud was due to the fact the compensation demanded by one tribe for a rape that was allegedly committed by a member of the rival tribe six months ago remained unpaid.
Clashes between tribes are common in Timika, home to one of the world's richest gold mines. A protracted conflict in 2006 killed 18 people and another between tribes in Kwamki Lama claimed eight lives in 2007.
Editor: Fang Yang