TerryShane Stone, 31, Ronald Rigby, 53, and Nathan Isaac, 29, died hen a car crashed down a bank and into the Mohaka River near Wairoa on Saturday. A fourth man survived the 150m fall and it's thought the men's car may have been run off the road by another vehicle.
He said police were still looking for sightings of a blue Japanese-made car that they suspect may have been involved in the incident.
Extra staff were being brought in to Wairoa this weekend to monitor the tangi of the men who died in the crash.
"Police will be monitoring the event and will respond if necessary to any trouble," a statement said.
Inspector Dean Clifford said police had received no reports of clashes between rival gangs following the crash and the rumour mill had been "working overtime".
"We urge everyone to calm down and stop spreading rumours about things that have not actually happened.
"If there are gang flare-ups or confrontation, police will deal with it appropriately."