Anti-government riots last week in Lhasa and a crackdown by communist authorities have led to calls by Tibetan activist groups to stop the relay from going through the region before the games.
"The Tibet leg of the torch relay will proceed as scheduled," said Jiang Xiaoyu, the executive vice president of the Beijing organizing committee.
Last week's riots, which the government says killed 16, have cast a larger spotlight on China's human rights record, though there have been no calls by governments or international sports officials for a boycott of the Olympics.
Even before the violence, taking the torch to the top of Everest was shaping up to be one of the most politicized feats of an already politicized Olympics. The relay hits on one of China's most sensitive issues: its often harsh 57-year-rule over Tibet.
Beijing says Tibet is historically part of China, but many Tibetans argue the Himalayan region was virtually independent for centuries and accuse China of trying to crush Tibetan culture by swamping it with Han people, the majority Chinese ethnic group.
Tibetan activist groups have criticized the Olympic torch run as an attempt by Beijing to add legitimacy to Chinese control of Tibet.
Jiang said climbers would take the Olympic flame to Everest's 29,035-foot summit in May.