Papua New Guinea wants Australia to axe Paladin's $423-million contract for security work on Manus Island.
On his first sitting day since being elected, Prime Minister James Marape addressed the issue in parliament, according to journalists in the country.
Local media reports Mr Marape said he did not want foreign companies working on security in the country when local businesses could be used.
"We don't intend for foreign security companies to engage in businesses including security," he told the parliament on Tuesday.
The Australian government is due to renew a multi-million dollar contract extension at the end of the month.
Labor senator Kristina Keneally is demanding Home Affairs Minister Peter Dutton release the findings of a review into an almost $500 million contract to manage the Manus Island offshore processing centre.
However, a formal review of the contract was ordered this year after the opposition learned Paladin was awarded the contract despite .
Foreign Affairs Minister Marise Payne was in Papula New Guinea this week to further strengthen Australia's relationship with its neighbour.
At the time, she said she looked "forward to seeing more Papua New Guineans working with Australian employers under the Pacific Labour Scheme".
Advocacy group Refugee Action Coalition said on Monday morning that had reached a "crisis point", after reports of two more incidents of self-harm within hours of each other.
