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Sergeant Steve Watt, of Queenstown, said the men were roped together on a route called The Grand Traverse, which traverses the summits of Single Cone and Double Cone.
The pair were on a guided climb with Wanaka-based Aspiring Guides.
Its general manager Jess Marriott said the company was "doing everything we can" to support the police investigation in to the incident.
WorkSafe is also making initial inquiries.
Sgt Watt said police and ambulance were notified at 11.45am.
St John South Island communications advisor Gerard Campbell earlier told the Otago Daily Times ambulance had not been involved in the incident.
A helicopter with a search and rescue crew on board was dispatched to the mountain.
Sgt Watt said one body has been recovered and police are working to recover the second.
"Our inquiries are continuing and we're working on notifying next of kin.''