A renowned U.S. mountain guide has achieved the rare Mount Everest region "triple crown" of climbing the Everest, Lhotse and Nuptse peaks in one season, a hiking firm said on Friday, as the season's death toll on the world's highest mountain hit 12.

Garrett Madison, 44, climbed Lhotse, the world's fourth tallest peak at 8,516 metres (27,939 feet) on Thursday, a day after he made his 13th ascent of Everest, at 8,849 metre (29,032 feet), said Ishwari Paudel of the Himalayan Guides company, which is helping Madison with logistics.

Madison, who owns the company Madison Mountaineering based in Seattle, climbed the smaller but technically difficult Nuptse peak, at 7,855 metres (25,770 feet), on May 8.

"It is very difficult to climb all three peaks in a single season and only a few other mountaineers have done it," Paudel said.

Separately, Department of Tourism official Khim Lal Gautam said Canadian national Petrus Albertyn Swart, 63, who fell sick in the "death zone" while going to Everest summit died on Thursday, taking the season's total death toll on the mountain to 12. At least three other climbers are missing or out of contact.

Hiking company official Paudel said Madison was accompanied by three sherpa climbers on all three peaks.

"We are extremely proud of the team and this tremendous accomplishment," Madison said on his company website.

British climber Kenton Cool, who climbed the triple crown in 2013, said Garrett was an "unflappable expedition leader" who quietly goes about his job.

"When I climbed what became known as the Triple Crown in one season I said it wouldn't be done again for 10 years," Cool told Reuters in a text message.

"I'm happy now that 10 years later it's Garrett who has managed to achieve the same feat ... bravo!!"

Cool, 49, last week set a new record of 17 summits of Everest, the world's highest peak, by a foreign climber.

A Nepali, Kami Rita Sherpa, this week climbed Everest for a 28th time, the most by any mountaineer.