text: Mr Trump's transition team said he and Tsai Ing-wen noted "close economic, political, and security ties" in a phone call.
  The move risks angering China, which sees Taiwan as a breakaway province.
  Chinese Foreign Minister Wang Yi dismissed the call as a "petty trick" by Taiwan, Chinese state media said.
  Mr Trump tweeted on Friday that Ms Tsai had called him to congratulate him on winning the US election.
  His team said that the US president-elect had also congratulated Ms Tsai on becoming the president of Taiwan last January.
  It is highly unusual for a US president or president-elect to speak to a Taiwanese leader directly.
  Following media reports pointing out the risks of angering China, Mr Trump tweeted: "Interesting how the US sells Taiwan billions of dollars of military equipment but I should not accept a congratulatory call."
  The White House has said Mr Trump's conversation does not signal any change in US policy.
  Mr Trump's spokeswoman said he was "well aware" of US policy towards Taiwan.
  Read more: What's behind the China-Taiwan divide?
  The split between China and Taiwan goes back to 1949, when the Republic of China (ROC) government fled the mainland to Taiwan. After 1945, it held China's seat on the UN Security Council and was, for a while, recognised by many Western nations as the only Chinese government.
  But in 1971, the UN switched diplomatic recognition to Beijing and the ROC government was forced out. Only a handful of countries now recognise Taiwan's government.
  Washington cut formal diplomatic ties with Taiwan in 1979, expressing its support for Beijing's "One China" concept, which states that Taiwan is part of China.
  China has hundreds of missiles pointing towards Taiwan, and has threatened to use force if it seeks independence.
  President Tsai, Taiwan's first female leader, led the Democratic Progressive Party (DPP) to a landslide victory in the January 2016 election.
  The DPP has traditionally leaned towards independence from China. President Tsai's administration does not accept the One China policy.
  Read more: Tsai Ing-wen, Taiwan's shy but steely leader
  Mr Trump's decision to turn his back on four decades of US protocol on Taiwan and speak directly to a president of Taiwan will stun policymakers in Beijing.
  Since his election last month, they have struggled to understand who is advising Donald Trump on Asia and what his China policy will look like.
  This move will turn concern into alarm and anger.
  Beijing sees Taiwan as a province. Denying it any of the trappings of an independent state is one of the key priorities of Chinese foreign policy.
  Read more from Carrie: The Trump phone call that will stun Beijing
  The Chinese Ministry of Foreign Affairs said it opposed any official interaction or military contact between the US and Taiwan, according to the People's Daily, a Communist Party mouthpiece.
  Foreign Minister Wang Yi said the conversation between Mr Trump and Ms Tsai was "just a petty trick by Taiwan" that he believed would not change US policy toward China, state media reported.
  "The One China policy is the cornerstone of the healthy development of China-US relations and we hope this political foundation will not be interfered with or damaged," he was quoted as saying.
  Despite the cut in formal ties nearly four decades ago, the US has still maintained friendly non-official relations with Taiwan.
  Following Mr Trump's telephone conversation, the White House said the US remained firmly committed to its "One China" policy.
  "Our fundamental interest is in peaceful and stable cross-strait relations," said Ned Price, a spokesman for the White House National Security Council.
target: US President-elect Donald Trump has spoken directly with the president of Taiwan - breaking with US policy set in 1979, when formal relations were cut.