Phillips, along with Jayda, 11, Maverick, nine, and Ember, eight, were spotted from a distance by a 16-year-old pig hunter, according to local media.
They were wearing camouflage gear and large camping backpacks – while the fugitive father was also reportedly seen holding a gun.
The foursome have been missing since December 2021, when police say Phillips took his children to an “unknown location”.
The children’s mother Cat said she was overjoyed by the sighting but also “overwhelmed” – as she called on Phillips to hand himself in to the police.
She told the New Zealand Herald newspaper: “It doesn’t get any easier… It’s been nearly three years.
“It was like Christmas come early and I really thought they would be coming home this time.”
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However, after Phillips and the children were spotted on Thursday, police are yet to locate them despite deploying a military helicopter and other resources.
Cat hit out at the official response to the sighting, describing it as “lacking”.
She added: “More should have been done, instantly… How can there not be more effort put in?
“It’s a confirmed sighting and yet nothing has come of it.”
Earlier this summer police offered $80,000 (£37,000) for information about the missing family members, although the deadline for the reward has now expired.
Since 2021 there have been numerous sightings, including in November 2023 when a suspect thought to be Phillips was caught on CCTV stealing a quad bike from outside a rural home.
Police also suspect he was involved in an armed robbery of a bank in Te Kuiti in May 2023, with officers later issuing a warrant for his arrest.
Detective Inspector Andrew Saunders said: “While we cannot go into detail, we want to reassure the public that we have the resources in place to respond to any information or reports of sightings that come in.
“Our focus is very much on the safe return of Jayda, Maverick and Ember to their whānau [family] and we are doing all that we can to make that happen.”