The water level suddenly increased, triggering a strong current that caused one of the rafts to flip over, local police chief Gusti Ngurah Yudistira said.
The five tourists who had been riding in it tried to reach the second raft, causing it to overturn, too, sending all 10 tourists into the raging waters, Yudistira said.
Two local rafting guides with them managed to rescue nine of the tourists, but Neil went missing.
Yudistira said authorities have notified villagers along the river to pay attention in their daily activities and immediately report to authorities if they see a body.
The tourists all wore life vests and helmets and had been briefed by guides before starting the 12-kilometer (7.4-mile) rafting trip, which was to last about 2 1/2 hours with a break midway down the river, Yudistira said.
The search involves about 70 rescuers from Bali’s Search and Rescue Agency, police and the rafting company’s guides, Sudiarsa said.