BEIJING  A team of climbers trudged through snow and ice to carry the Olympic torch to the summit of Mount Everest on Thursday, fulfilling a long-held goal of the Chinese government to have the Olympic flame lit on top of the world’s highest mountain.

Overseas groups opposed to Chinese rule in Tibet quickly denounced the event, saying the Chinese government was simply using the torch relay to bolster claims of sovereignty over what should be an independent country.

The ascent of the north face of Mount Everest, whose icy summit is more than 29,000 feet high, was the most ambitious leg of the Olympic torch relay. The torch that climbers carried to the top at 9:18 a.m. on Thursday was a side torch; the main torch is making its way through the southern province of Guangdong and will continue through every province of China before arriving in Beijing in early August.

The Chinese government has tried to maintain tight control over every aspect of the Everest climb. Officials brought a group of journalists to the base camp to help publicize the ascent while barring foreign climbing groups from any summit attempts for fear of Tibet-related protests further marring the torch relay, which has already been beset by anti-China demonstrations in foreign cities. Nepal, prompted by Chinese leaders, has also kept climbing groups away from the mountain.