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.

The New Zealander -- a professor at an Australian university -- and two Papua New Guinea nationals were taken hostage at gunpoint last Sunday in a remote and densely forested region of the country.

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

Marape said the hostages had been freed after "covert operations" and said 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."