A visitor to the area, which is home to significant yellow-eyed penguin and fur seal populations and a popular visitor stop for that reason, contacted the Otago Daily Times this week to complain about the state of the area.
Jackie Trotter, of Geraldine, said she and a friend left "appalled at the state of the place" after a visit on January 2.
"I was quite shocked — there were thousands of rabbits there — there were so many, just hopping all over the place," she said.
At her last visit, at the beginning of 2014, rabbit numbers were "nowhere near" what they were now.
Upoko Runaka o Moeraki chairman David Higgins said the problem was not just at Katiki.
Thistles were spread across Otago and rabbits had set in across the entire peninsula at Moeraki.
"Quite frankly, I think everyone is p...ing in the wind," he said.
"I shot 42 rabbits the other day and I was nowhere near Katiki Point. They are all over the peninsula. You can’t isolate Katiki Point just because somebody is worried about the penguins, or something."
Katiki Point is largely Ngai Tahu land under the customary care of Te Runanga o Moeraki. About 2ha of public conservation land is managed by the Department of Conservation (Doc).
"You get thistles after the spring we’ve had — with warm temperatures and a bit of rain — and away the thistles go," Mr Higgins said.
The runanga had a pest eradication programme in place — two hunters shot rabbits — but they were fighting an uphill battle. He said the runanga, like many, was awaiting a virus to be introduced by the New Zealand Rabbit Co-ordination Group.
Otago Regional Council director of environmental monitoring and operations Scott MacLean said the group, of which ORC was a member, hoped to import the Korean strain of the rabbit haemorrhagic disease virus (RHDV1-K5) at Moeraki, which was a "priority site".
Last year, he told the Otago Daily Times it was the "landowner’s responsibility to control pests on their land".
The programmed release, pending import approvals, would be in the autumn. Rosalie Goldsworthy, manager of Penguin Rescue, which looks after the birds at Katiki, said she took care of the land until the runanga took over in 2014.
"All I can do is look out the window at the rabbits and the thistles."
She added she decided against poisoning rabbits, which can ringbark trees penguins use as protection on the point, as a threatened New Zealand falcon had taken up residence at her reserve and she did not want to poison its prey.
Doc operations manager Annie Wallace said the department was aware of the pests at Katiki Point and Doc was working with Ngai Tahu — both in Christchurch and at Moeraki — towards a solution.