A New Zealand father who spent nearly four years on the run with his children was killed in a police shootout on Monday, authorities said.

Tom Phillips, who absconded with his three children in December 2021 after a row with his former partner, died in the rolling hill country of the North Island's Waikato region.

His case captivated the country, particularly in the Waikato area and the town of Marokopa where Phillips was suspected of hiding.

The family has eluded capture for nearly four years despite several sightings, including CCTV apparently showing Phillips and a child breaking into a store last month.

Police said they were called in the early hours of Monday morning about a potential burglary at a store by two people on a quad bike.

"Knowing the information that we had previously had, that had seen Tom Phillips also in this area, additional staff were called out and responded to that location," New Zealand Police Acting Deputy Commissioner Jill Rogers said.

Police used road spikes to stop the quadbike, which then veered off the road into a bank.

When police approached, Phillips shot an officer in the head with a high-powered rifle. They fell to the ground and called for back up.

"A second patrol unit arrived and has engaged the offender, and he has died at the scene," Rogers said.

The officer who was shot was airlifted to hospital and was undergoing surgery. (AFP)