They were alerted to the fall by satellite phone around midday from a guided climbing party, who met the victim's climbing partner on the mountain.
Melchior said the rescue team had to be very careful in the "extremely hazardous" conditions. Three professional mountain guides were flown in by helicopter 200m away from the body. They were able to climb over to the body and bring it back to a place the helicopter could land.
"There's a reason climbers go out very early, everything is frozen. As the sun comes out it starts to loosen.
"They were working at the bottom of a 200m rock face which has extreme dangers of rockfall in a very crevassed area.
"The recovery went extremely well from our point of view, except for the fact he unfortunately didn't survive the fall."
The climbing partner was an Australian man who was not injured. The pair had only recently met for the purposes of climbing the mountain. Melchior said the climbing partner was deeply shaken by the incident.
"He's obviously deeply shocked. He's being taken care of."
Melchior said this was the seventh incident the team had been called out to in a week. He said it was usually a busy time of year but this was unusually busy. They had attended a variety of incidents from kayakers in trouble on a lake, to a hang glider who had an accident and a tramper who rolled their ankle.
"Obviously this is an enormous workload for a wholly volunteer organisation that depends on donations."
Wanaka Police Search and Rescue coordinator Sergeant Aaron Nicholson said the climber's death was a tragedy following the successful rescue of two other fallen climbers in the last week.
"The very busy start to the summer outdoor season is a sobering reminder of the inherent risks in mountaineering.
"Our thoughts are with the man's family," Nicholson said.
Weather Watch head analyst Philip Duncan said the conditions were good today. There were light winds, with only a risk of showers and temperatures hovered between 4C and 21C.
While there was no apparent severe weather, Duncan said conditions could change very quickly.
"Just a passing cloud can give you zero visibility."
Last week two injured climbers were rescued after they fell 200m on Mt Aspiring. They were on the southwest route and fell down a steep area of snow and ice above the Bonar Glacier.
A second party of four climbers travelling in a similar direction found them two hours later. They set off their personal locator beacon to get help.
Three helicopters were used to assess the scene and take the climbers to Dunedin Hospital with moderate injuries including broken bones.
Mt Aspiring is known to be a technically difficult climb. The northwest ridge is the most commonly climbed route on the 3000m peak.
A 24-year-old woman died last year when she fell crossing a waterfall face in Mt Aspiring National Park. A 21-year-old man slipped and fell to his death in 2014.
In 2008, Kathmandu co-founder John Pawson, 48, fell 800m to his death on Mt Aspiring. The well-known Wanaka businessman was climbing the southwest ridge of the mountain with award-winning photographer and writer Martin Hill when he fell.
The pair were not roped together and Hill was left stranded about 200m from the summit.
In 2005, three people died on the mountain in 10 days.
Consul for the Czech Republic Vladka Kennett said she hadn't been contacted by authorities yet but she may be needed to liaise with the climber's family.
Kennett sheltered Pavlina Pizova, who survived a harrowing month in a remote cabin, snowed in and alone after watching her partner Ondrej Petr, 27, die on the Routeburn Track earlier this year.
She said these sorts of incidents were incredibly sad for the family. But she tried to deal with it as "professionally and humanely as possible".
