Police were alerted after the climbers made it to a remote alpine hut and called the Department of Conservation on Tuesday afternoon.
A police spokesperson today said rescue teams had not been able to reach the pair because of the weather.
"The weather is continuously being reviewed for a suitable weather window, and search and rescue personnel are on standby," they said.
"Agencies involved remain in communication with the two people who have sufficient food and water for an extended stay.
"The two climbers are being provided medical advice from specialist medical experts."
The Doc website said the route to the 12-bunk Empress Hut was highly technical and only suitable for very experienced mountaineers.
MetService's forecast for Mount Cook showed high cloud increasing through the day, with showers developing this afternoon and northwesterlies, strong at times.
