Donald Trump is yet to speak directly with the leader of Asian and global powerhouse China, and the President’s “worst call by far” phone conversation with Malcolm Turnbull could be to blame.

In the absence of a direct conversation, the US President broke the ice with Xi Jinping on Thursday by writing the Chinese President a letter.

The letter thanked Xi for his congratulatory note on Mr Trump’s inauguration and wished the Chinese people a prosperous Lunar New Year of the Rooster, the White House said in a statement.

“President Trump stated that he looks forward to working with President Xi to develop a constructive relationship that benefits both the United States and China,” it said.

Despite China responding by saying it attached great importance to China-US ties, there is reportedly a hesitance to take Mr Trump’s call.

Trump sends Xi a letter pic.twitter.com/RFlzvKh9df

— Zeke Miller (@ZekeJMiller) February 9, 2017

China’s official Xinhua News Agency quoted foreign ministry spokesman Lu Kang on Thursday as saying China is willing to work with the US to advance ties, noting shared interests in promoting peace and prosperity.

Mr Trump and Mr Xi spoke soon after the billionaire businessman won the US presidential election in November, but are yet to officially converse as heads of state, despite the US President holding conversations with at least 18 other world leaders.

Reuters quoted diplomatic sources in Beijing as saying “China has been nervous about President Xi being left humiliated in the event a call with Trump goes wrong and the details are leaked to the US media”.

The Washington Post last week published details about Mr Trump’s acrimonious phone call with Mr Turnbull, which the President reportedly described as his “worst call by far” to leaders that day.

Mr Turnbull did not elaborate on reports the President was angered by the US agreement to accept refugees from Manus Island and Nairu, saying only they shared “very frank and forthright discussions in which of each of us has expressed our views”.

After details of the conversation were leaked, Mr Trump further strained US-Australia relations by publicly tweeting about the discussion, describing the refugee relocation agreement as a “dumb deal”.

“That is the last thing China wants,” a source familiar with China’s thinking on relations with the United States told Reuters.

“It would be incredibly embarrassing for President Xi and for Chinese people, who value the concept of face.”

A senior non-US Western diplomat told Reuters that China was unlikely to be in a rush to set up such a call.

“These things need to happen in a very controlled environment for China, and China can’t guarantee that with the unpredictable Trump,” the diplomat said.

“Trump also seems too distracted with other issues at the moment to give too much attention to China.”

Among the contentious areas that China fears Mr Trump could “go off script” were the issues of Taiwan sovereignty and trade.

Mr Trump angered China in December when he took a phone call from Taiwan President Tsai Ing-wen, contrary to a long-standing US protocol not to officially speak with the Island’s leader.

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

— Donald J. Trump (@realDonaldTrump) December 3, 2016

China considers Taiwan a wayward province and rejects its right to hold formal diplomatic relations with other countries.

During his election campaign, Mr Trump threatened to impose tariffs on Chinese imports and accused Beijing of deliberately devaluing its currency to effect a trade imbalance.

He has also criticised China’s leaders for failing to do more to rein in North Korea’s nuclear ambitions.

China has been taking out massive amounts of money & wealth from the U.S. in totally one-sided trade, but won't help with North Korea. Nice!

— Donald J. Trump (@realDonaldTrump) January 2, 2017

The US has also inflamed the issue of sovereignty in the South China Sea by vowing to defend “international territories” in the strategic waterway.

“The most worrying aspect about the new presidency is his temperament, not his policy,” Wang Fan, director of China Foreign Affairs University’s Institute of International Relations, told Bloomberg.

“We’re worried he’d go to the extreme.”