A Tibetan woman took the Olympic torch the last steps to the top of Everest on Thursday, realising "a dream of all Chinese people", but rights groups criticised Beijing for politicising the Games.

"Long live Tibet!" and "Long live Beijing!", the climbers, all wearing red, shouted joyously into a TV camera after unfurling the Chinese national flag, the Olympic flag and a flag bearing the Beijing Olympic logo.

The ambitious project to take the torch to the Himalayan peak was cast as the highlight of the relay ahead of the Games, which start in exactly three months' time, and followed weeks of protests against Beijing's rule in Tibet.

"We have realised a promise to the world and a dream of all the Chinese people," base camp commander Li Zhixin told reporters after being mobbed by jubilant friends and colleagues.

Communist China has spent billions of dollars on staging the Olympics, eager to project the image of a modern and vibrant country. But protests during the international leg of the torch relay have bruised Chinese pride and provoked a surge of nationalist sentiment.

Overseas pro-Tibet groups condemned China for taking the torch to the world's highest peak. "Beijing's conquest of Everest is a political move meant to reassert China's control of Tibet," Tenzin Dorjee, deputy director of Students for a Free Tibet, said in a statement e-mailed from New York. The Free Tibet Campaign said on its website the project was "a callous attempt (by China) to legitimise its baseless claims to sovereignty over Tibet".