A spokesman for Seven Summit Treks, a Nepal-based company that helped organize some of Mr. Purja’s expeditions, said by phone that it was in touch with his climbing team and confirmed that he had reached the top of Shishapangma.

The attempt to be the fastest to reach the top of all the world’s known mountains over 8,000 meters, or about 26,350 feet, which Mr. Purja called Project Possible, started in April, when he scaled Annapurna. He then quickly tackled the 13 remaining mountains, all of which are in the Himalayan and Karakoram ranges that stretch across China, India, Nepal and Pakistan.

Climbing the world’s 8,000ers, as they are known, requires time in the so-called death zone, an altitude at which reduced oxygen levels make it difficult for humans to breathe effectively and where climbers can die.

The previous speed record for scaling all 14 peaks was held by Kim Chang-ho of South Korea, who completed his climbs in seven years, 10 months and six days. He narrowly broke an earlier record held by Jerzy Kukuczka of Poland, who took seven years, 11 months and 14 days .

Mr. Kim later died in a storm on the Mount Gurja in Nepal, and Mr. Kukuczka died in 1989 while trying to scale the south face of Lhotse in Nepal.