The climbers, attempting to reach the mountain summit in Canterbury, did not meet their prearranged transport on Monday morning and were reported missing.
A helicopter and search and rescue teams could not find the group that afternoon, before bad weather halted the search.
The climbers have been named as 56-year-old Kurt Blair, Carlos Romero, 50, from the United States, and a Canadian national.
Aoraki area commander Inspector Vicki Walker said in a statement late this morning that the terrain on the mountain was difficult to navigate.
“I want to acknowledge the work so far of those involved in the search, including the Department of Conservation (Doc) Search and Rescue Team, The Helicopter Line, and Police Search and Rescue."
The team would continue to assess weather conditions, however at this stage it remained unlikely the search would be able to continue before Thursday.
Earlier, Walker told RNZ's Morning Report programme that searchers spoke to a party coming down the ridge who said the missing men were going up the route and intending to get to the summit.
She could not confirm a report that the trio had suffered a fatal fall, but said police held "grave concerns" for the missing party.
Search teams on Monday found an ice axe and a jacket belonging to the men, who were believed to be ascending via the Zurbriggen Ridge.
Walker said searchers spoke to a party coming down the ridge, who said the climbers were going up the route and intending to get to the summit.
Police were not able to release the name of the Canadian man at this time, due to family wishes.
Mountain Safety Council chief executive Mike Daisley said climbing conditions were good at the time the trio were expecting to attempt the summit. The poor weather had come in after they were due out of the area.
Daisley said common hazards on Aoraki Mount Cook were avalanches, glacial crossings and rockfalls, and there were often icy surface conditions this time of year.
The weather had deteriorated significantly since the weekend, but no avalanches had been reported in the area, he said.
"It's a real tragedy, what looks to be unfolding."
However, there had been many examples of experienced climbers such as these surviving by finding snow caves or other shelter, he said.
"Not all hope is lost."
- RNZ and APL
