A veteran US climber and three Nepali guides completed the "triple crown" of Everest and two neighbouring peaks, expedition organisers said Friday, becoming only the second team to ever claim the feat in a single season.

The achievement came as a Canadian mountaineer's death took the toll from this climbing season on the world's highest mountain to 12.

Expedition leader Garrett Madison, 44, reached the summit of Lhotse, the world's fourth tallest peak at 8,516 metres (27,939 feet), on Thursday along with three Nepali guides, according to his local expedition organising partner.

"He climbed Lhotse yesterday a day after reaching his summit of Everest for the 13th time," Iswari Paudel of the Himalayan Guides company told AFP.

The team had summited the adjoining smaller but steep Nuptse, at 7,861 metres (25,791 feet), on May 8.

Only British climber Kenton Cool claims to have climbed all three mountains of the massif in a single season, in 2013.

On Everest, a Canadian climber became the 12th fatality this climbing season, Paudel said, while at least three others are missing.

The 64-year-old Canadian fell ill in the "death zone", the area above 8,000 metres where thin air and low oxygen levels heighten the risk of altitude sickness that is notorious for its difficult terrain.

On average, around five climbers die on the 8,849-metre (29,032-feet) mountain every spring.

But this year's toll has more than doubled that as the season draws to a close.

Nepal's tourism department said that searches were underway for at least three missing climbers.

Malaysian climber Muhammad Hawari Hashim, 33, who is hearing-impaired, went missing around Camp 4 last Friday after a successful summit.

"It has been a week, and there is little hope of survival for someone missing that high," said Pasang Sherpa of Pioneer Adventure, his expedition organiser.

On the same day, a Singaporean climber also went missing above 8,000 metres, reportedly falling towards the northern side of the mountain.

Another Nepali climber has been out of contact since Thursday.

In all, seven foreigners and five Nepalis have lost their lives on Everest this year, while according to Nepal's tourism department nearly 600 climbers have summited the mountain.

It has issued 478 permits to foreign climbers, with each paying an $11,000 fee.

Since most will need a guide, more than 900 people -- a record -- were expected to try to summit during the season, which runs until early June.