Papua New Guinea's prime minister has ordered an investigation into allegations that businesses operating in PNG have links to international terrorism.

Prime minister Peter O'Neill said the allegations were of a financial nature and did not pose any threat to the people of PNG.

But Australian authorities said they were unaware of any terrorist threats.

Mr O'Neill's announcement followed a front-page story in PNG's Post Courier newspaper, claiming an Australian family with links to terrorism was operating a business in the country.

The paper did not identify the family, but said they had invested in logging, security services and agriculture in PNG.

The Post Courier cited "top-secret documents" and "the intelligence community" as the source of the information about the alleged terrorist link.

Mr O'Neill responded to the story, saying the government "is taking action to rid Papua New Guinea of people with terrorist links".

"The prospect that businesses in our country could be involved with financing of these deplorable groups is alarming," Mr O'Neill said, referring to the Islamic State in Iraq and Syria.

"Our intelligence agencies are working with security partners in other countries to deal with this cross-border issue.

"The important point for Papua New Guineans to know is that there is no evidence of activities by groups or individuals that could lead to terrorist incidents on our soil."

The exact nature of the allegations remains unclear. The Australian High Commission in Port Moresby released a statement distancing itself from the allegations.

"We are not aware of any Australians in PNG who are suspected of involvement in terrorism," it said.

"If Australian authorities had any information about a threat to PNG's security, we would inform the appropriate authorities in PNG immediately.

"Australian authorities are not aware of any such threat."