By Stephen Collinson, Nicole Gaouette and Elise Labott CNN

(CNN) -- China's top diplomat has labeled a controversial phone call between President-elect Donald Trump and Taiwan's President "a shenanigan by the Taiwan side," amid concern the call could anger Beijing even before Trump takes office.

China views Taiwan as a renegade province and, since 1979, the US has acknowledged Beijing's claim that Taiwan is part of China, with US-China relations governed by a set of protocols known as the One China Policy.

This means there are no formal diplomatic relations between the United States and Taiwan -- so Friday's exchange could risk a major upset.

While Chinese Foreign Minister Wang Yi indicated Taiwan was behind the "shenanigan" in his comments Saturday, he also signaled that Beijing does not want this to augur a shift in established US policy.

"It won't at all change the 'one China' structure that the international community has agreed upon," Wang said when he was asked about the call on the sidelines of a foreign policy seminar.

"I don't think it will change the 'one China' policy that U.S. administrations have adhered to over the years. The 'one China' policy is the cornerstone of a healthy China-U.S. relationship. I hope this political foundation won't be disrupted or damaged."

First time in decades

Trump's transition team said Friday that the President-elect had chatted with the Taiwanese President Tsai Ing-wen, who passed along her congratulations.

"During the discussion, they noted the close economic, political, and security ties (existing) between Taiwan and the United States. President-elect Trump also congratulated President Tsai on becoming President of Taiwan earlier this year."

The chat marks the first publicly reported call between a US President or President-elect and the leader of Taiwan since Washington established diplomatic relations with Beijing in 1979, said Bonnie Glaser, a China expert at the Center for Strategic and International Studies.

It is perhaps the first major sign of the unpredictability that Trump has vowed to bring to long-held US relations with the rest of the world.

The call, first reported by the Financial Times, risks throwing US-China relations into a tailspin before Trump takes the oath of office on January 20.

China's state-run CCTV quickly issued a statement saying Trump made "an unprecedented break with the One-China Policy and accepted US-Mainland protocol."

It added, "The Mainland says it firmly opposes official contact in any form between Washington and Taipei."

Trump on Friday night emphasized that Taipei initiated the call.

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

He soon followed up by tweeting, "Interesting how the U.S. sells Taiwan billions of dollars of military equipment but I should not accept a congratulatory call."

Taiwan's President on Friday night published a statement about the phone call on an official website, which she described as an "intimate and relaxed conversation" lasting 10 minutes.

The two also shared their views on important policy points, the statement said, according to a translation, "in particular, to promote the domestic economy and strengthen national defense, allowing the people better lives and a guarantee of security. The two briefly exchanged opinions on the situation in the Asia region."

Kellyanne Conway, Trump's campaign manager, told CNN's Anderson Cooper on "AC360" that she wouldn't go beyond what the transition team statement said. But the President-elect was fully aware of the call's implications, Conway suggested.

"He either will disclose or not disclose the full contents of that conversation but he's well aware of what US policy has been," Conway said.

'No change'

By Friday night, China had already reached out to the Obama administration. White House officials declined to comment on diplomatic discussions.

Ned Price, a spokesman for the US National Security Council, said "there is no change to our longstanding policy on cross-Strait issues."

"We remain firmly committed to our 'one China' policy based on the three Joint Communiques and the Taiwan Relations Act," he said. "Our fundamental interest is in peaceful and stable cross-Strait relations."

A different Obama administration official said there was no contact with either the White House or State Department about the call beforehand.

Stephen Yates, a fellow at the Heritage Foundation who is an adviser to Trump's transition team, is in Taiwan and helped facilitate the call, according to a source familiar with the visit. Yates was an Asia adviser to former Vice President Dick Cheney and is very supportive of Taiwan.

Earlier Friday, China's Foreign Ministry Spokesman Geng Shuang had warned about the need for the United States to respect the One China policy, "be cautious in handling the Taiwan issue and never turn back the wheel of history, lest the overall situation of China-U.S. relations be impaired."

Meanwhile, former US Secretary of State Henry Kissinger met with China's President Xi Jinping Friday, China's state-run news agency Xinhua reported.

Kissinger -- secretary of state from 1973-77 -- is credited with secret diplomacy that helped Nixon open up Communist China to America and the West.

During their Beijing meeting, Kissinger told Xi "that he believes it is the expectation of the U.S. new administration to facilitate sustained, stable and better growth of U.S.-China relations.," Xinhua reported.

'Major pivots'

The United States acknowledged China's claim that there is one China and that Taiwan is part of China in a joint communique signed in 1979 at the time of the formal establishment of relations between Washington and Beijing.

Chris Murphy, a Connecticut Democrat who sits on the Senate Foreign Relations Committee, publicly blasted Trump for his actions in a series of tweets.

While it will soon be Trump's right to shift policy, alliances and strategy, Murphy said, "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."

He added that "if they aren't pivots - just radical temporary deviations - allies will walk if they have no clue what we stand for. Just as bad."

CNN's Daniella Diaz, Michelle Kosinski, Nanlin Fang, Steven Jiang and Joe Sterling contributed to this report.

TM & © 2016 Cable News Network, Inc., a Time Warner Company. All rights reserved.