US President Donald Trump has broken the ice with Chinese President Xi Jinping in a letter that said he looked forward to working with him to develop relations, although the pair haven't spoken directly since Trump took office.

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

"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.

China said on Thursday it attached great importance to China-US ties after confirming it received the letter.

At a daily press briefing in Beijing, Chinese Foreign Ministry spokesman Lu Kang said China commended Trump for sending Lunar New Year greetings to the Chinese people and said co-operation between the two countries was the only option.

Trump and Xi have yet to speak directly since Trump took office on January 20, although they did talk soon after Trump won the US presidential election in November.

Diplomatic sources in Beijing say China has been nervous about Xi being left humiliated in the event a call with Trump goes wrong and the details are leaked to the US media.

Last week, US ties with staunch ally Australia became strained after the Washington Post published details about an acrimonious phone call between Trump and Prime Minister Malcolm Turnbull.

"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 said 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."

There are a number of contentious areas where China fears Trump could go off script, the diplomat said, pointing in particular to the issue of self-ruled Taiwan, as well as trade.

Trump upset China in December by taking a phone call from Taiwan President Tsai Ing-wen. China considers Taiwan a wayward province with no right to formal diplomatic relations with any other country.

Trump has also threatened to slap tariffs on Chinese imports, accusing Beijing of devaluing its yuan currency and stealing US jobs.

In his Senate confirmation hearing, US Secretary of State Rex Tillerson said China should not be allowed access to islands it has built in the disputed South China Sea.

The White House also vowed to defend "international territories" in the strategic waterway.

China has repeatedly said it has smooth contacts with the Trump team.

The Foreign Ministry in Beijing said last week the two countries were remaining "in close touch".