A New Zealander and two other hostages have been freed in Papua New Guinea, the country's prime minister said Sunday, after they were held for a week in the highlands by an armed group.

"It took us a while but the last three has been successfully returned," Prime Minister James Marape said in a statement.

Police said they were returning to the capital Port Moresby with the three freed hostages Sunday afternoon, where Marape would greet them.

The New Zealand man -- a professor at an Australian university -- and two Papua New Guinea women were taken hostage at gunpoint last Sunday in a remote and densely forested region.

Police had been negotiating with the hostage takers, who initially demanded a ransom of US$1 million -- an enormous sum in one of the Pacific's poorest nations -- before dropping the asking price and abandoning a 24-hour deadline.

Earlier this week, the captors released another woman who was part of the group of academics and guides that had been kidnapped at gunpoint.

At the time, police said the three captives were "in reasonable health, though are being held in difficult terrain."

Marape said the hostages had been freed after "covert operations" and the original ransom demand had not been met -- but did not provide further details.

"We apologise to the families of those taken as hostages for ransom," Marape said.

"To criminals, there is no profit in crime. We thank God that life was protected."

Papua New Guinea's highlands are a sprawling expanse of jungle-cloaked hills where the central government and security forces have little sway.

In recent years, the regions have seen an increase in tribal warfare and modern weapons.