New Zealand's police say they will investigate how a father vanished into forest with his three children for years without detection, even as law enforcement expanded a search for them.

A New Zealand man who evaded authorities with his three children for nearly four years has been shot and killed by police.

Police in New Zealand offered an 80,000 New Zealand dollar reward and immunity from prosecution on Tuesday to anyone who could help them secure the safe return of three children missing since December 2021.