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It was not immediately clear whether Trump's telephone call with Tsai Ing-wen marked a deliberate pivot away from Washington's official "One China" stance, but it fuelled fears he is improvising on international affairs.
China regards self-ruling Taiwan as part of its own territory awaiting reunification under Beijing's rule, and any US move that would imply support for independence would likely trigger fury.
Xi meets Taiwan opposition leader, stresses 'One China'
During Friday's discussion, Trump and Tsai noted "the close economic, political and security ties" between Taiwan and the United States, according to the president-elect's office.
"President-elect Trump also congratulated President Tsai on becoming President of Taiwan earlier this year," it said.
Beijing on Saturday offered a robust response.
"We have already made solemn representations about it to the relevant US side," the Chinese foreign ministry said.
"It must be pointed out that there is only one China in the world. Taiwan is an inalienable part of China's territory,"
China also urged "relevant parties in the US... to handle Taiwan-related issues with caution and care to avoid unnecessarily interfering with the overall situation of Sino-US relations."
Trump, who had come under fire for the telephone call, hit back -- on Twitter.
"Interesting how the US sells Taiwan billions of dollars of military equipment but I should not accept a congratulatory call," Trump tweeted.
President Barack Obama's White House said the outgoing US administration had not changed its stance on China-Taiwan issues.
"There is no change to our longstanding policy on cross-Strait issues," National Security Council spokeswoman Emily Horne told reporters.
"We remain firmly committed to our 'One China' policy," she added. "Our fundamental interest is in peaceful and stable cross-Strait relations."
Washington cut formal diplomatic relations with the island in 1979 and recognises Beijing as the sole government of "One China" -- while keeping friendly, non-official ties with Taipei.
But since coming to office this year, Tsai has refused to accept the "One China" concept, prompting Beijing to cut off all official communication with the island's new government.
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Tsai's Democratic Progressive Party government (DPP) defeated the Kuomintang (KMT), which had much friendlier ties with Beijing, in a landslide election victory in January.
Even before the call with Taiwan, Trump's unorthodox diplomatic outreach had raised eyebrows, and, for some critics, in extending his hand to Taiwan, Trump crossed a dangerous line.
"What has happened in the last 48 hours is not a shift. These are major pivots in foreign policy without any plan. That's how wars start," tweeted Democratic Senator Chris Murphy.
In China, analysts painted the call as something originating from Taiwan, claiming it was a deliberate Taiwanese attempt to upend America's China policy.
Jin Canrong, from China's Renmin University, told AFP Tsai had been "very cunning" in her call to Trump.
"Tsai Ing-wen would like to draw the United States against the mainland," he said.
During his presidential campaign, Trump repeatedly accused China of manipulating its currency to harm US manufacturing and threatened to impose tariffs on some of its exports.
"One can see at once that Trump is very reckless, not familiar at all with the whole context," Jin said.
Chinese citizens were quick to react to the call on social networking platforms, noting Trump's reference to Tsai as "president" whereas on the mainland she is only referred to as Taiwan's "leader".
"The US dares to recognise Taiwan independence," one user said on Weibo, China's version of Twitter.
Another posted: "He calls Tsai as +president+ on Twitter!!! Is Trump thinking of using Taiwan as a bargaining chip in his negotiations with China?"
However Zhang Wensheng, of Xiamen University, was more circumspect, dismissing Trump's use of the term "president" as "personal greetings" that "do not reflect a political position whatsoever".
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