The call was the first such contact with Taiwan by a U.S. president-elect or president since President Jimmy Carter adopted a one-China policy in 1979.
Trump said on Twitter that the Taiwanese leader initiated the call. "The President of Taiwan CALLED ME today to wish me congratulations on winning the Presidency. Thank you!" he said.
Alex Huang, a spokesman for Tsai, said: "Of course both sides agreed ahead of time before making contact."
The Trump 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 cooperation.
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.
The call comes at a time of worsened Taiwan-China relations since the election of Tsai’s pro-independence Democratic Progressive Party (DPP) earlier this year.
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 call and did not want to be identified said Chinese officials he spoke to beforehand said they were not troubled by the call because Trump was not yet president. Trump takes office on Jan. 20.
Tsai was one of four world leaders Trump spoke to on Friday, raising questions about whether he is effectively coordinating with the U.S. State Department before reaching out to leaders overseas.
Gerrit van der Wees, a former Dutch diplomat who lobbies on behalf of Taiwan, said the call indicated Trump would be less bound by conventions and restrictions in foreign policy and was “signaling a broader change in U.S. policy towards Taiwan.”
"SEAT OF HIS PANTS"
Advisers to the Republican president-elect have indicated that he is likely to take a more robust policy toward China than Obama, a Democrat, and that Trump plans to boost the U.S. military in part in response to China's increasing power in Asia. However, details of his plans remain scant.
Senator Chris Murphy, a member of the Senate Foreign Relations Committee, said Trump was entitled to change policy, but his approach was potentially dangerous.
"Foreign policy consistency is a means, not an end. It's not sacred. Thus, it's Trump's right to shift policy, alliances, strategy," Murphy, a Democrat, said in a note on Twitter.
But he added: "What has happened in the last 48 hours is not a shift. These are major pivots in foreign policy w/out any plan. That's how wars start."
Also on Friday, Trump invited Philippines leader Rodrigo Duterte to the White House next year during what a Duterte aide said was a "very engaging, animated" phone conversation. Duterte has openly insulted Obama, who canceled a planned meeting with him in September.
A statement issued by Trump's transition team made no mention of the invitation. The transition team said that Trump also spoke on Friday to Afghan President Ashraf Ghani and Singapore Prime Minister Lee Hsien Loong.
Winston Lord, who was U.S. ambassador to China from 1985-89 and is a former assistant secretary of state for East Asian and Pacific affairs, said the strategic importance of the Taiwan call was unclear.
"Like so many things with Trump, who knows? This man is ignorant about foreign policy and is flying by the seat of his pants, so it is difficult to assess the significance.
"Having said that, I have no problem with his talking to Madame Tsai; Taiwan is a good friend and although our relations are unofficial, I think it’s important to maintain close bonds with Taiwan."
Trump and Chinese President Xi Jinping spoke by telephone on Nov. 14. Xi stressed that cooperation was the only choice for relations between the world's two largest economies, and Trump said that the two had established a "clear sense of mutual respect."
Trump lambasted China throughout the U.S. election campaign, drumming up headlines with pledges to slap 45 percent tariffs on imported Chinese goods and label the country a currency manipulator on his first day in office.
Douglas Paal, a former official of the U.S. National Security Council who served as U.S. representative to Taiwan from 2002-2006, said nothing Trump had said in the campaign suggested he wanted to rebuild the relationship with Taiwan at the expense of the China relationship.
"From the information I have so far, this is a standalone item," Paal said, "but the Chinese will feel the need to make a major protest so there isn’t more of this."
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(Additional reporting by Valerie Volcovici, David Alexander, Yara Baroumy, John Walcott, Arshad Mohammed, Jeff Mason and JR Wu; Writing by David Brunnstrom and Jeff Mason; Editing by Jonathan Oatis and Leslie Adler)
