Four people, including an Australian-New Zealand archaeologist, were conducting fieldwork in a remote PNG region when they were captured by an armed group earlier this week.
Speaking on the sidelines of the Pacific Islands Forum in Nadi, Justin Tkatchenko said negotiations to see the group continued.
"So far, so good," he told AAP.
One hostage, who Mt Tkatchenko confirmed was a woman and who the ABC reports was the program co-ordinator, has been released.
The archaeologist is an Australian-based academic who has New Zealand citizenship.
Mr Tkatchenko said a wide range of authorities in PNG were involved in negotiations to free the group.
"Our police force, our defence, our negotiators from the government side through the leadership of our minister for internal security," he said.
"It's a combined effort to look at the opportunistic situation by these people and see what their real intentions are.
"We don't at all support these kinds of activities and the full force of the law will go down on those that have carried out these acts that society does not tolerate."
While hopeful the talks would be fruitful, Mr Tkatchenko said he couldn't promise the hostages' release.
"I can't guarantee anything," he said.
The ABC reports the hostages have been moved between villages in the area.
Their captors are asking for a ransom from the Australian and New Zealand governments.
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