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 constructive relations, although the pair haven't spoken directly since Trump took office.

Trump also issued belated well-wishes to China for the Lunar New Year, the most important holiday in the world's most populous nation. He had been the only US president in recent years not to have issued greetings when the holiday fell on January 28, triggering speculation in China as to whether it was an oversight or an intentional slight.

A statement from the White House late on Wednesday said Trump wrote to Xi wishing the Chinese people greetings for the new year and the Lantern Festival that falls on Saturday.

"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," the statement said.

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The letter also thanked Xi for his congratulatory letter on Trump's inauguration and wished the Chinese people a prosperous Year of the Rooster, it said.

Chinese Foreign Ministry spokesman Lu Kang said China commended Trump for sending Lunar New Year greetings to the Chinese people and said cooperation between the two countries was the only option.

Wang Yiwei, a professor of international relations at Beijing's elite Renmin University, said the letter suggested the new US administration wanted to signal the importance it attached to the US-China relationship, without risking being confronted on specific issues.

"Trump has sent many messages that makes the world confused, like on the South China Sea and 'One China' policy, so if he makes a phone call President Xi will ask 'What do you mean?'," Wang said.

"He wants to avoid this, so he just sends a letter for the first step."

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.

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

Trump has accused Beijing of unfair trade practices and currency manipulation, criticised China's military buildup in the South China Sea, and accused Beijing of doing too little to pressure neighbour North Korea over its nuclear and missile programmes.

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He also upended four decades of diplomatic protocol by speaking by phone with Tsai Ing-wen, the president of Taiwan, which China claims as its own territory.

Beijing decried the phone call with Tsai and has rejected the other accusations. China has in fact been spending heavily from its pile of foreign currency reserves to prop up the value of its currency, which would make its exports less competitive.

The prospect of a military confrontation over the South China Sea had also been raised by Trump's chief strategist Steve Bannon when he hosted the conservative Breitbart News Daily radio show in 2015 and 2016.

Bannon said he envisioned the possibility of a US-China war over the strategic waterway within five to 10 years. China, which claims the sea virtually in its entirety, has been building man-made islands in the area and equipping them with airstrips and military installations.