He had been described as an experienced tramper, but he had no emergency locator beacon on him.
Search coordinator Sergeant Mike Fitzsimons said the team was coming in tonight after a fruitless search.
Tomorrow a local rescue helicopter would again join the teams, after poor weather grounded it today.
Rough weather over the last few days had made the hunt difficult and police now had "grave concerns" for Mr Levi's safety, Mr Fitzsimons said.
The area is riddled with caves, with New Zealand's longest cave system the Bulmer Cavern running 66km through Mt Owen, and its jagged marble terrain and dense bush make the search tough going.
"The Bulmer Caves are one of the most extensive in the world and there is a group of about 13 cavers who had organised another exploratory trip tomorrow.
"They're aware of what we've been doing and our situation and they'll be keeping an eye out for him."
Mr Fitzsimons said the rescue volunteers had given up their Christmas Day and Boxing Day to look for Mr Levi.
"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."