"His apparent appropriation of skeletal material without legal authority, without respect for tangata whenua, or indeed without any of the basic decorum with which any reasonable person would hope that human remains are afforded, is deplorable," NZAA president Katharine Watson said yesterday.
Assertions that prior to the settlement by the ancestors of Maori, New Zealand was inhabited or visited by people of Welsh, Celtic, Phoenician, Chinese and Egyptian origins were unsupported by any current archaeological, historical or biological research, she said.
In May the reported Mr Hilliam's latest controversial claims - that British experts had established that skulls he had in his possession were of Welsh and Mediterranean origin.
Mr Hilliam said the experts came to New Zealand to do the testing, during which time he also took them to five sites in the North Island to look at, photograph and "work" on skeletons.
"I couldn't get anyone in New Zealand to do it. The experts had to come to New Zealand to physically examine them."
He would not name them or the institution's where they work.
Yesterday, he said he had also presented the forensic pathologist - "one of the top 10 in the world" - with teeth for DNA testing.
Mr Hilliam said he had dug up, recorded and photographed human remains in 1996 and 2016, and had since returned them, but would not reveal their location.
Heritage NZ's investigation focused on whether human parts had been taken out of New Zealand, not the testing itself, he said.
Mr Edwards said there were legal protection provisions regarding archaeological sites and human remains.
Fines for destroying an archaeological site without Heritage NZ authority could be up to $300,000 per event, depending on circumstances.
Ms Watson said all sound archaeological, genetic, linguistic and genealogical evidence supported the theory that New Zealand was first settled by deliberate, planned voyaging, around 700-800 years ago by groups of east Polynesian people.
"There is no conspiracy, as Mr Hilliam and his supporters claim, to suppress archaeological evidence of earlier, non-Polynesian settlement of any kind; the evidence just does not exist,'' he said.
Mr Hilliam said after his story about the facial reconstruction broke he received more than 500 messages from around the world, mostly people asking why the authorities in New Zealand "continued to deny its real history".
Regarding his claim that "overseas experts" had proved the Welsh origins of pre-Maori settlers, Mr Hilliam said he will "let it ride for now."