The footage was shot on 3 October in a bush area of Marokopa, with police becoming aware of it at about 19:00 local time (06:00 GMT) that day. That prompted a three- day search involving police and army helicopters.
In the video, Tom Phillips can be seen leading his children through the rugged terrain. They are all wearing camouflage clothing.
Speaking to the New Zealand Herald newspaper, external on Thursday, the mother of the children, Cat, expressed her relief that they were still alive and that her children appeared well enough to be carrying their own bags.
She accused her ex-partner of using the children as “pawns in his game”.
“They shouldn’t have to be worrying about where they’re going to sleep that night or whether they’re going to be warm,” she told the paper.
She also said authorities should be doing more to track down her ex-partner, and appealed to those she believed were helping her ex-husband.