Tapsell said the last time any bones were found on Newdicks Beach was about two weeks ago, and that was why the decision was made not to extend the six-week rāhui.
"But it is very important if anyone does find more bones to immediately call the police and the police will then notify us," he said.
Tapsell urged people to treat any discovery of human remains with respect and sensitivity and store them carefully in a plastic bag or container until police could collect them.
Tapsell said no decision had been made about where the remains should be reburied and more discussions would be needed to find an appropriate place.
It was believed the remains are pre-1900 in origin. Ōkurei Point was the location of several Māori pā sites, he earlier said.
Tapsell said he was still in talks with Heritage New Zealand's Tauranga archaeologist Rachel Darmody about dating the bones, and he hoped funding could be made available.
"Being able to do so would be like putting faces to this mystery and possibly also give us an insight into how these people died," he said.