"Feracon's staff member who carries out possum control in the area is not to blame," Presland said.
"Third-party investigations have already established that the birds did not ingest possum bait."
A council investigation showed the birds are likely to have been poisoned with Alphachloralose, which sends the affected animal into a state of hypothermia.
The poison can be purchased by the general public and is not used by Feracon for possum control.
Green Bay Vets and the Bird Rescue organisation, which have been managing the birds' health since they were found, agreed with the findings.
"Threats against our staff and contractors will not be tolerated and need to stop immediately," Presland said.
"I understand emotions are high, but this act of cruelty is nothing to do with Feracon who work hard to protect bird life in the Waitakere Ranges through possum control."
The police have been contacted over the posts made on the Cornwallis, Huia and Parau Community Facebook Page.
Auckland Council has urged anyone with details or information relating to the poisoning of these birds to call 09 301 0101.
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