(CNN) Donald Trump anchored his presidential campaign on defying convention and flouting political norms, and it worked better than anyone ever expected.

But now the President-elect is applying the same unorthodox, off-the-cuff style of leadership to sensitive diplomatic procedure and it's causing a storm at home and overseas.

Trump flew in the face of four decades of international protocol and precedent Friday when he became the first President or President-elect known to speak directly to the leader of Taiwan since the US established formal relations with Beijing in 1979.

The conversation with President Tsai Ing-wen caused a diplomatic crisis with Beijing, sent shock waves through the foreign policy establishment in Washington and caused concern around Trump's looming presidency.

The stunning move raised fundamental questions about how Trump's foreign policy inexperience and brash style as a disruptor will translate to the intricacies of international statecraft, where an ill-advised phone call or off-message sentence can cause a diplomatic incident.

Trump's volatile, unexpected moves during his unconventional campaign made him an elusive target for his political foes, and often saw him take policy positions, or reverse them, on the hoof.

But surprises and unpredictability could be less well suited to great power diplomacy, and the world is watching nervously to see how Trump adapts.

Three international calls raising questions

JUST WATCHED Trump's Taiwan call: reckless or reasonable? Replay More Videos ... MUST WATCH Trump's Taiwan call: reckless or reasonable? 05:08

There have now been three incidents in a week that have raised questions about Trump's emerging foreign policy.

Friday's call left some China-watchers wondering whether Trump was sending a shot across the Asian giant's bows and previewing a significant shift in US adherence to the "One China" policy that has helped prevent a clash between the US and China over the nationalist island.

The China kerfuffle came as Trump's calls with Philippine President Rodrigo Duterte and Pakistani Prime Minister Nawaz Sharif put his unorthodox style on display and appeared to hint at changes in foreign policy under his presidency.

Trump's critics say the President-elect and his team have not put in the preparation needed for a successful foreign policy.

Veteran US diplomat Christopher Hill, assistant secretary of state for East Asia and Pacific affairs during the George W. Bush administration who also worked for Republican and Democratic presidents, said the Trump team made a huge mistake with the Taiwan call.

"Obviously, it was an example of what is all too often happening now with this incoming administration. This tendency to wing it," Hill said.

Delaware Sen. Chris Coons, who sits on the Foreign Relations Committee, said on CNN's "Smerconish" Saturday that the call with Tsai raised questions about Trump's appreciation of diplomatic etiquette.

"We will have to see whether this is the beginning of a new chapter where the President-elect, after he is inaugurated, conducts a foreign policy that is shoot from the hip Twitter-storm-style ... where he ... takes unscheduled calls from foreign leaders, which break with decades of precedent."

He continued, "Or whether he relies on the advice of career professionals in the State Department and makes moves in a calculated and thoughtful way."

Vice President-elect Mike Pence said Sunday on NBC's "Meet the Press" however that the furor over the call was a "tempest in a tea pot." Pressed by host Chuck Todd on whether anything should be read into the call Pence said: "Well, I don't think so."

A relationship with global implications

The ties between the United States, the world's sole super power, and China, a dominant Asian juggernaut, are often referred to as the most important bilateral relationship in global politics.

The nations are interlinked by a vast web of economic connections, have massive trading exchanges and China maintains vast holdings of dollar-denominated US debt. In recent years, China's more assertive posture under President Xi Jinping has led to rising security tensions, between Washington and its allies and Beijing, in the South and East China Seas.

JUST WATCHED Why it's so tense in the South China Sea Replay More Videos ... MUST WATCH Why it's so tense in the South China Sea 01:17

So Trump's first foray into US-China relations was always going to be closely watched. But no one predicted it would raise questions about whether he was committed to US policy stances going back to President Richard Nixon.

In an odd twist, Nixon's secretary of state Henry Kissinger met with Xi Friday in Beijing for a pre-scheduled meeting, according to China's state-run news agency Xinhua.

Trump will have wide latitude to reorient US foreign policy as he sees fit when he is inaugurated -- after all he won a democratic election after a campaign in which he proposed sweeping shifts to the America's global role.

"This is the President-elect. This will be his administration. He will be commander-in-chief and he will be President of the United States imminently now," Trump senior adviser Kellyanne Conway told CNN's Anderson Cooper on Friday.

The last week suggests that Trump wasn't joking when he pledged to make US foreign policy more "unpredictable."

He raised doubts during the campaign about the US commitment to NATO, said US allies like South Korea and Japan should pay more for US protection and has signaled he will seek to forge better relations with Russia.

With that backdrop, Trump's call with Tsai will likely foment fresh concern among US allies that he intends to disrupt the international system upheld by the US for decades.

Trump alters trajectory of Obama's foreign policy legacy

Trump's transition team dismissed claims by Democrats that Trump either did not understand the implications of the Taiwan call — or that he is ignoring the advice of US national security officials.

Conway said Trump had made "dozens and dozens" of phone calls with world leaders that had gone "really well" and said he was "well aware of what US policy has been on Taiwan."

Still, there are few signs so far that Trump's call on Taiwan or other foreign policy interventions are the result of a thought-out global strategy rather than his own freewheeling style of leadership.

That perception will likely increase pressure on the President-elect to complete his nascent national security team with his nominee for secretary of state in the coming days.

Several Republicans, who believe President Barack Obama has been an unassertive US leader warmly praised Trump's call with Tsai.

"I would much rather have Donald Trump talking to President Tsai than to Cuba's Raul Castro or Iran's Hasan Rouhani. This is an improvement," said Texas Sen. Ted Cruz on Twitter , referring to two leaders pursued by Obama in his policy of engaging US foes.

I would much rather have Donald Trump talking to President Tsai than to Cuba's Raul Castro or Iran's Hasan Rouhani. This is an improvement. — Ted Cruz (@tedcruz) December 3, 2016

Arkansas GOP Sen. Tom Cotton said in a statement that Trump was doing the right thing.

"I commend President-elect Trump for his conversation with President Tsai Ing-wen, which reaffirms our commitment to the only democracy on Chinese soil. I have met with President Tsai twice and I'm confident she expressed to the President-elect the same desire for closer relations with the United States."

What Trump's response portends

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

"Interesting how the U.S. sells Taiwan billions of dollars of military equipment but I should not accept a congratulatory call."

Trump has a point. But his tweet ignores the strategic ambiguity built into the US compact with China over Taiwan, which allows Washington to offer the island the means for its defense without recognizing it diplomatically in a way that could spark a confrontation with Beijing.

For now, China appears to be taking the view that Trump's intervention was the result of a green foreign policy team -- not a looming policy shift -- despite making clear its displeasure and restating the "One China" policy in a statement. Chinese officials also contacted the White House for an explanation about the Trump call.

The official China Daily, which reflects government policy, warned against over-interpreting the call between Trump and Tsai.

JUST WATCHED Amanpour on Trump's diplomacy Replay More Videos ... MUST WATCH Amanpour on Trump's diplomacy 04:31

"For Trump, it exposed nothing but his and his transition team's inexperience in dealing with foreign affairs," the paper said in a commentary that appeared to reflect hopes the new President would eventually settle into the established pattern of US-China relations.

Still, no one in Trump's team has reaffirmed the One China policy since the telephone call.

Hill, the former State Department Asia hand, told CNN's Erin Burnett on Friday that Washington could not afford a spat with China over Taiwan at the start of the Trump administration.

"We have a lot of stuff going on with China -- South China Sea, North Korea -- we don't need this now," he said.