China has lodged a "stern" diplomatic protest after US President-elect Donald Trump spoke by phone with the president of Taiwan.

Not since President Jimmy Carter adopted the so-called "one China" policy in 1979 has a US president or president-elect spoken directly with a leader of Taiwan, a self-governing island.

China dismissed the call as a "petty action" by the self-ruled island it claims as its own.

Image: Taiwan's President on the phone to Mr Trump at her office in Taipei

Mr Trump also spoke on the phone with Rodrigo Duterte, in what was described by a close aide of the Philippines president as a "very engaging, animated conversation".

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In a series of tweets, Mr Trump defended his decision to break with decades of US diplomatic precedent by speaking to Taiwanese president Tsai Ing-wen.

Mr Trump said Ms Tsai initiated the call.

"The President of Taiwan CALLED ME today to wish me congratulations on winning the Presidency. Thank you!"

Alex Huang, a spokesman for Ms Tsai, said: "Of course both sides agreed ahead of time before making contact."

Interesting how the U.S. sells Taiwan billions of dollars of military equipment but I should not accept a congratulatory call. — Donald J. Trump (@realDonaldTrump) December 3, 2016

About an hour later, Mr Trump tweeted another post, saying: "Interesting how the US sells Taiwan billions of dollars of military equipment but I should not accept a congratulatory call."

Mr Trump's transition team said in a statement that the two leaders noted that "close economic, political and security ties exist between Taiwan and the United States".

Taiwan's presidential office said the two leaders touched on strengthening bilateral interactions and establishing closer co-operation.

There was no immediate comment from China, which is likely to be angered because it views Taiwan as a renegade province.

Washington is Taiwan's most important political ally and sole arms supplier, despite the lack of formal diplomatic ties.

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The White House responded to the call by saying that "longstanding policy" on China and Taiwan has not changed.

"We remain firmly committed to our 'one China' policy," said Ned Price, a national security spokesman for President Barack Obama.

"Our fundamental interest is in peaceful and stable cross-Strait relations."

A former diplomat who helped arrange the phone call and did not want to be identified said Chinese officials he spoke to beforehand said they were not troubled by the call because Mr Trump was not yet president.

Washington cut formal diplomatic relations with Taiwan in 1979 and recognises Beijing as the sole government of China, while keeping friendly non-official ties with Taipei.

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But since coming to office this year, Ms Tsai has refused to accept the 'one China' policy, prompting Beijing to cut off all official communication with the island's new government.

Ms Tsai's pro-independence Democratic Progressive Party government defeated the Kuomintang, which had much friendlier ties with Beijing, in a landslide election victory in January.

In a video released by Mr Duterte's close aide, Bong Go, the Philippines president told Mr Trump of his desire to "enhance the bilateral ties between our two countries".

Mr Trump invited Mr Duterte to visit The White House next year and received an invitation to attend an East Asian summit to be hosted by the Philippines next year.

Mr Duterte has kept up his anti-US rhetoric for months, even calling Mr Obama a "son of a whore" for raising concerns over his drugs crackdown which has led to the deaths of 4,000 suspected drug dealers and users.

The volatile leader has also threatened to scale back the presence of US troops in Philippine military camps, established by Mr Duterte's predecessor as a counterbalance to China's military assertiveness.