Nepal is home to eight of the world's highest peaks.
The 36-year-old's body was found after he died in his sleep in a tent at 7,400 metres on the 8,850-metre mountain.
Legendary Japanese climber found dead on Mount Everest
Only hours after an Australia woman climbed Mount Everest for the second time in two years, two other adventurers died while attempting to summit the world's tallest mountain.
The Japanese climber was identified as 35-year-old Nobukazu Kuriki and the Macedonian as 63-year-old Gjeorgi Petkov. Kami Rita's father was among the first professional guides after Nepal opened to foreign trekkers and mountaineers in 1950. According to the report, more than 340 foreign climbers are allowed by Nepal to ascend the peak during the current season.
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Mr Rita was 24 when he first climbed Mt Everest in 1994 and he has climbed the 8,850m (29,035ft) mountain nearly every year since then. He was not successful in climbing Everest and lost most of his fingers due to frostbite during an attempt in 2012.
Teams must end their attempts by the end of this month as conditions are set to deteriorate. They did not have other details about his death.
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Lam, who was in his 40s, reportedly fell ill on Sunday when his group neared Everest Base Camp, at about 5,000 metres above sea level. The next year, an quake triggered another avalanche that ripped through Base Camp, killing 19 people. In 2014, an avalanche at the Khumbu Icefall killed 16 Sherpa guides.
Around 400 people have so far reached the summit of Everest as the busy spring climbing season - which runs from April to May - gets into full swing.
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