A recovery operation was launched before being called off on the evening of 29 July.
“The recovery of the body under the current prevailing conditions of rockfalls and changeable weather on Laila Peak is attached to a high risk and not achievable,” the statement continued.
“Laura enriched the lives of many with her warm and straightforward manner.
“She showed us that it is worth standing up for your dreams and goals and always staying true to yourself.”
The German Olympic Sports Confederation said Dahlmeier was “more than an Olympic champion – she was someone with heart, attitude and vision”.
International Olympic Committee president Kirsty Coventry said Dahlmeier’s death is “deeply shocking for all of us in the Olympic movement”.
She added: “She lost her life in her beloved mountains. She will be remembered forever.”
German President Frank-Walter Steinmeier said Dahlmeier was an “ambassador for our country around the world and a role model for peaceful, joyful and fair coexistence across borders”.
Dahlmeier, an experienced mountaineer, represented Germany at two Winter Olympics, winning two golds and one bronze medal in Pyeongchang in 2018.
She was the first woman to win the sprint and pursuit events at the same Games and won a further 15 medals, including seven gold, across five World Championships before retiring from competition in May 2019.
