Relations at stake
Bush met the Dalai Lama despite China's warning that US plans to honour the exiled Tibetan spiritual leader could damage relations between Beijing and Washington.
The meeting was held on the eve of a congressional award ceremony for the Dalai Lama.
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China routinely criticises visits abroad by the Dalai Lama, who fled Tibet for India in 1959.
Winner of the 1989 Nobel Peace Prize, he remains popular among Tibetans and is widely respected abroad.
China claims Tibet has been its territory for centuries, but many Tibetans say they were independent for most of that period.
Beijing has also bitterly denounced plans for the Dalai Lama to receive the Congressional Gold Medal on Wednesday.
Bush is scheduled to attend the ceremony on Capitol Hill.
China regards the spiritual leader of Tibetan Buddhists and a Nobel Peace Prize laureate as a separatist and a traitor.
Zhang Qingli, the Communist Party boss in Tibet, on Tuesday said the Dalai Lama "had tried to split the motherland".
"We express our firm opposition and grave objection. ... We feel very angry about this," he said on the sidelines of the Communist party congress in Beijing.
"We are furious. If the Dalai Lama can receive such an award, there must be no justice or good people in the world."
The White House denied that Bush's private meeting with the Dalai Lama - the president's fourth since taking office - was meddling in China's internal affairs.
Dana Perino, the White House spokeswoman, said: "We understand that the Chinese have very strong feelings about this."Bush is to speak at the presentation of the medal, whose recipients have included Mother Teresa, Nelson Mandela and Pope John Paul II.
She explained that Bush gave his Chinese counterpart, Hu Jintao, early notice about him attending the awards ceremony and the Bush administration took pains to keep the meeting between low-key in an apparent bid to placate China.
China pulled out of a meeting this week at which world powers were to discuss Iran, in apparent protest at congress's plan to honour the Dalai Lama with its highest civilian award.
China had also cancelled an annual human-rights dialogue with Germany to show displeasure over Chancellor Angela Merkel's September meeting with the Dalai Lama.
Yang Jiechi, the Chinese foreign minister, said China had expressed "resolute opposition" to the US award.
He said: "China has solemnly demanded the United States cancel the above-mentioned and extremely wrongful arrangement."
Melissa Chan, Al Jazeera's correspondent in Beijing, said: "Tibet is one of China's biggest liabilities in terms of the country’s global public image.
"Unfortunately, the Tibet cause will only pick up interest and momentum as China prepares to host the world’s biggest public event, the Olympics, next year."