''At this stage we have no idea where she is. We are relying on our community to possibly spot them," said detective senior sergeant Greg Turner of Mills.
Mr Turner said police were interested in any sightings of the SUV with a registration plate FQS965.
''We are talking with family, friends, and members of the community to try to locate her and try to encourage Mrs Mills to present herself to the police station."
Police are keeping tight-lipped over the relationship between the woman and the children.
People who knew the whereabouts of Mills were asked to contact Tauranga Police Station on 07 577 4300 or CrimeStoppers on 0800 555 111.