"We are trying to find the next of kin now and arrange repatriation. It's still very much in the early stage," she said.
Flanderova said Czechs who came to New Zealand are generally experienced travellers, but "sadly cases like this happen from time to time".
Honorary consul for the Czech Republic in New Zealand, Vladka Kennett, who also runs a travel agency, described it as a "very sad" accident.
"Czechs love the outdoors, especially young people. They travel the European alps for mountaineering and climbing and so they are more likely to be out there doing it, rather than sightseeing trips. They do love it here," she said.
"There are a lot of Czechs in the country at the moment, which means the probability of something happened is probably higher than in the past."
The weather at the time was thought to have been good.
Melchior said the man may have slipped.
"In those environments the margin of error is effectively nil," he said.
The Wanaka Search and Rescue alpine rescue team found and recovered the man's body yesterday afternoon in an operation that took more than three hours.
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 by helicopter to about 200m from the body.
They climbed to the body and brought 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," Melchior said.
"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 didn't survive the fall."
Melchior said the climbing partner was deeply shaken by the accident.
"He's obviously deeply shocked. He's being taken care of."
Melchior said this was the seventh rescue the team had been called to in an unusually busy time.
They had helped kayakers in trouble on a lake, a hang glider who had an accident and a tramper who rolled an 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 after 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.
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 stranded about 200m from the summit.
In 2005, three people died on the mountain in 10 days.
