"While they were last seen in the Catlins, the reality is they could be anywhere in the southern South Island," he said.
"We really want to resolve this situation. John can call me via 03 471 4800 at any stage and talk with me personally about his situation."
They are thought to be travelling in a dark blue Volkswagen Touareg station wagon, registration number DUY263.
Mike is of solid build and Asian descent. John Beckenridge is 1.75m tall, of medium build, and is of Swedish descent.
Anyone who sees the pair should phone 111 immediately. To report information phone the Southern District Command Centre on 03 471 5002, or Crimestoppers anonymously on 0800 555 111.