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The Dunedin City Council has been negotiating with the receiver of a mining firm to buy the fossil-rich site and protect it for scientific research.
However, a purchase has still not resulted from 18 months of negotiations and scientists have not had access in the meantime.
Save Foulden Maar spokeswoman Andrea Bosshard said the drive towards public ownership needed to continue for the benefit of future generations.
She cautioned councillors against losing sight of the big picture, that there was immense public benefit associated with the site.
"It’s crucial we get those scientists back on site again."
The maar has a wealth of fossils of insects, leaves, fish and flowers and two of just five fossilised orchids in the world.
It could also help people understand and cope with the impacts of climate change, Save Foulden Maar chairwoman Kimberley Collins said in a written submission on the council’s 10-year plan.
"Foulden Maar contains a detailed climate record unique to the southern hemisphere and is the only site in the world known to record the de-glaciation of Antarctica with high accuracy," Ms Collins said.
Ms Bosshard said the geological importance of the area was becoming well known.
Scientists carried out some research at the site before mining firm Plaman Resources went into receivership in 2019, when the arrangement ceased, and Ms Bosshard expected public ownership would lead to an escalation in scientific inquiry.
However, wider access would need to be managed carefully.
"We can’t have people swanning in for a little dig."
The lobby group has suggested limited and guided tour groups and a presentation of information at the Middlemarch Museum.