Updated 8.39pm: Police say the last text messages sent by the step-father of a missing Invercargill boy gave a feeling of 'goodbye'.

Mike Zhao Beckenridge has been missing since the middle of last month, when John Beckenridge picked him up from his Invercargill school.

AUDIO: Detective Senior Sergeant Mark McCloy on the case

The last confirmed sighting of of the pair was in the in the Catlins, in the days after they initially went missing.

But police say all evidence now points to this being a murder-suicide at Curio Bay where Beckenridge's car was found in the water.

Detective Sergeant Mike McCloy had this to say when asked about a murder-suicide.

"That's one of the possibilities. We are very much hoping that isn't the case, and myself and the investigation team are working really hard based on the possibility that Mike and John are still out there."

Detective sergeant Mark McCloy says they believe the vehicle was driven off the cliff at high speeds.

He says the wheel marks stop a couple of metres short of the cliff edge.

"And the vehicle marks in a typical paddock which is pretty rough and undulating are pretty straight, and we believe the car has been airborne prior to the edge of the cliff."