John Beckenridge's vehicle appears to have been driven at "high speed" off a Southland cliff, which could indicate a grim outcome for the missing man and his 11-year-old stepson, police say.
The pair disappeared from Invercargill on March 13 after Mr Beckenridge picked up Michael Zhao-Beckenridge from his Invercargill school.
Mr Beckenridge, 64, had a parenting order against him forbidding contact with the boy.
His car has since been discovered at the bottom of Curio Bay in the Catlins.
Today, Detective Sergeant Mark McCloy said there were a number of factors that indicated it was a murder-suicide case.
Those factors included no confirmed sightings of the pair outside the Catlins area, the use of Mr Beckenridge's cellphone in the Catlins area on March 20, and the conclusion by police staff that the vehicle would have been driven off the cliff at a high speed due to the track marks and where it initially went airborne.
"However, until we can confirm this police still hold out hope that Mike and John are still out there and continue to investigate the matter as such."
He told TV3's Campbell Live show last night that there was still some doubt as to how anyone could commit such a crime.
"I just can't believe that someone would be so cruel, or so selfish, so self-centred ... to involve an 11-year-old child in that, and commit such an act," he told the programme.
Mr McCloy said Mr Beckenridge had sent a series of text messages on March 20 to his neighbour, his friends, his solicitor and, finally, "one was sent to Mike's mother".
It was unlikely the pair would have been able to leave the Catlins without "substantial help from other parties", he said.
And, if they had been in the car when it left the cliff, their bodies might also never be recovered, given the history of body recovery following mishaps in the area, he indicated.
"Not one body's ever been recovered," he told Campbell Live.
Police had so far been unable to recover Mr Beckenridge's vehicle from Curio Bay because of rough weather and tidal conditions.
As soon as conditions allowed, police would attempt to retrieve the vehicle, a police spokesman said earlier.
Police divers had been able to perform a "partial search" of the station wagon, which showed there was nothing inside.
"But ... there's only so much you can see with a partial search."
A number of doors were missing from the vehicle, he said.
A request by police to put a border alert on the pair was issued on the day they disappeared.
"If those passports, or people try to use passports associated with those names to leave the country, an alert is brought up on the screen," he said.
No alert had come through, which meant it was unlikely they had left the country, he said.
"[But] until we can confirm what may or may not be in the car, we are still looking at all potential possibilities that may have happened."
- Additional reporting: Otago Daily Times