China regards the spiritual leader of Tibetan Buddhists and a Nobel Peace Prize laureate as a separatist and a traitor.
"We are furious," Zhang Qingli, Tibet's Communist party boss, told reporters in China. "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."
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.
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"China has solemnly demanded the United States cancel the above-mentioned and extremely wrongful arrangement," Yang told reporters.
Liu Jianchao, a foreign ministry spokesman, said if the decision to honour the Dalai Lama was not reversed it would have an "extremely serious impact" on bilateral relations.
Bush is to speak at the presentation of the medal, whose recipients have included Mother Teresa, Nelson Mandela and Pope John Paul II.
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."
China is one of six nations that have offered Iran a deal to stop its disputed nuclear activities, and Wednesday's meeting in Berlin was part of the US-led drive to punish Iran for spurning the offer.
China is considered the main hurdle to US plans to impose new United Nations sanctions on Iran.
China and Russia, which have economic ties to Iran, have gone along so far with an international effort to coerce Iran away from an alleged weapons programme but negotiations on the next round of sanctions is expected to be difficult.
The six-nation diplomatic meeting is still expected to take place, perhaps a week later, said a US official who spoke on condition of anonymity.
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.