US President Barack Obama warned his successor Donald Trump on Friday against provoking a "very significant" response from China by reaching out to Taiwan.

Trump has broken with four decades of US diplomacy by suggesting Washington's "One China" stance may be reviewed and by accepting a call from Taiwan's President Tsai Ing-wen.

Beijing regards self-governing Taiwan as part of its sovereign territory and has already expressed anger at Trump's move.

Tension between the world's two greatest powers is running high, as was underlined Thursday when Chinese sailors seized an unmanned US naval probe in the South China Sea.

Obama, who leaves office on January 20 to make way for Trump, has taken a cautious stance with the Asian giant and urged the president-elect to proceed with care.

"The idea of One China is at the heart of their conception as a nation," he told reporters at an end of year news conference at the White House.

"And so if you are going to upend this understanding, you have to have thought through what the consequences are, because the Chinese will not treat that the way they'll treat some other issues.

"This goes to the core of how they see themselves, and their reaction on this issue could end up being very significant."

- 'Crush his own toes' -

On Monday, China's foreign minister Wang Yi warned that Beijing would not allow "any force in the world" to play tough with Beijing over its territorial claims.

In a shot across Trump's bows, Wang said anyone who "tries to sabotage the One China policy or harm China's core interests... will lift a rock only to crush his own toes."

A Chinese spokesman also warned the Taiwanese not to get any ideas, warning: "Facts will show those people that 'Taiwan independence' is a dead end."

Since Trump's declaration, China's Liaoning aircraft carrier battle group has conducted its first live fire exercises involving dozens of ships and aircraft.

Taiwan's defense minister, meanwhile, has urged young people to join the armed forces.

Trump took a congratulatory call from Tsai after he won the November 9 US presidential election, one of dozens he received from leaders around the world.

At first it was not clear whether he had done so without realizing that China would see it as an affront or whether it was a deliberate change in practice by his incoming administration.

But, challenged by critics over his apparently reckless move, Trump doubled down and insisted he would not accept China "dictating" to him over protocol.

And, resuming the attacks on Chinese trade policy he made throughout his campaign, he implied that US support for "One China" would depend on Beijing making concessions.

- Courtesy calls -

"I don't know why we have to be bound by a One China policy unless we make a deal with China having to do with other things, including trade," Trump told Fox News on Sunday.

Obama was careful not to condemn Trump's initiative out of hand, but warned that if ties between Beijing and Washington break down, both sides will be worse off.

"So I think it's fine for him to take a look at it," Obama said.

"What I have advised the president-elect is that across the board on foreign policy you want to make sure that you're doing it in a systematic, deliberate, intentional way."

And he implicitly criticized Trump's decision to make diplomatic moves without seeking the advice of the State Department and US intelligence agencies.

"My advice to him has been that before he starts having a lot of interactions with foreign governments other than the usual courtesy calls that he should want to have his full team in place," he said.

"He should want his team to be fully briefed on what's gone on in the past and where the potential pitfalls may be, where the opportunities are, what we've learned from eight years of experience."