He has been described as an experienced tramper but had no emergency locator beacon on him.
A local rescue helicopter was grounded yesterday due to poor weather but police hoped to have it back in the air today.
The area is riddled with caves - New Zealand's longest cave system, the Bulmer Cavern runs 66km through Mt Owen.
Mr Fitzsimons said the rescue volunteers had given up their Christmas Day and Boxing Day to look for Mr Levy.
"They do a great job and they're very skilled, dedicated people."
Nelson Marlborough Rescue Helicopter crewman Hamish Pirie was part of a team which flew over the mountain from 11pm on Christmas Day.
He said it was "extremely rugged" terrain they were looking at.
"It's marble, it's very broken ... there are deep crevasses, lots of holes into caves, lots of bluffs and drop-offs and extremely dense bush and steep terrain. The upper part is just hellish."