Mr O'Neill told members of the Port Moresby Chamber of Commerce and Industry on Thursday that he was "not in a hurry" to grant an extension to the mine -- whose permits expire later this year -- even though it provides a quarter of the country's export receipts.
Following a series of environmental problems, BHP -- which built the mine in the then-remote Star Mountains in PNG's Western Province in the early 1980s -- pulled out of the venture.
Through an agreement with the PNG government of the day that involved a form of indemnity over environmental damage, BHP placed 63.4 per cent of the ownership in the hands of PNG Sustainable Development Program, a trust that was chaired by leading economist Ross Garnaut.
Under the rules established a decade ago, two-thirds of the dividends that PNGSDP receives are held in a fund for use only after the mine's eventual closure. The figure has now reached $1.4 billion.
The other third goes into a development fund, which deploys about $100 million a year, of which a third is spent on projects in Western Province and two-thirds in the rest of the country.
In 2011, the mine paid $543m in taxes, about 16 per cent of the PNG government's income.
Last November, Professor Garnaut resigned as chairman of PNGSDP and was replaced by former prime minister Mekere Morauta.
Recently, BHP ceased appointing three of the seven PNGSDP directors.
They are now chosen by the board itself, which also includes PNG government nominees. But BHP must agree to any changes in the core terms of reference under which the trust operates.
Last month, OTML chief executive Nigel Parker told PNG's The National that more than 100,000 people in 156 villages had unanimously backed the extension of the mine's operations until 2025.
But this requires government approval. And Mr O'Neill told the Port Moresby chamber that those seeking the extension, particularly BHP through PNGSDP, had to clearly indicate to the government that the mine life extension would make a real change in the country.
"So far, I am not convinced," Mr O'Neill said.
The Prime Minister said he did not believe the parliament made the right decision 10 years ago in agreeing to the mine's new governance.
"We have given (BHP) protection from the environmental damage that caused misery for our people," he said. "This is not the sort of development I want to encourage. We are quite happy to wait" (for BHP to agree to changes in the mine ownership structure and governance). The resources are not going to run away."
A BHP spokesman said last month that the company "now has no association whatsoever with OTML or PNGSDP".
"BHP's preference was to close the mine early," the spokesman added.
"This was not acceptable to the PNG government which was concerned about the socioeconomic impacts of early closure. The PNGSDP is an independent company which has provided a lasting legacy for the people of PNG."