It was possible the tide would wash up more bones, he said.
A six-week rāhui was placed on January 14 and prohibits the collection of kaimoana or any other food from the area.
Tapsell said any discovered bones should be stored in a plastic bag or similar to protect them and police should be contacted immediately.
Bones were being held by the Te Puke police until decisions could be made about reinterment.
Tapsell said there were several pā sites at Ōkurei Point and the area was the first landing site in Maketū for Māori in the early 1340s.
He said he was in talks with an archaeologist from Heritage New Zealand about dating the bones.
Tapsell believed his whānau were relatives of the people who had been buried at the urupā and people as far afield as the South Island had been in contact to say they also believed they were descendants.
The disturbance of the urupā had upset many people and Tapsell urged people to adhere to the rāhui and any discovery of human remains with sensitivity and respect.
Heritage New Zealand's Tauranga archaeologist Rachel Darmody said the remains were understood to be pre-1900 in origin.
"But we do not know the exact date as no analysis of the kōiwi tangata has been carried out by an osteoarchaeologist.
"We are in ongoing contact with iwi and police regarding this matter and providing archaeological support as and when required."