US President Donald Trump has contacted China's President Xi Jinping in a letter saying he looked forward to working with him to develop relations.

The letter, the first direct contact Trump has made with President Xi since he took office, thanked the Chinese premier for his congratulatory note on his inauguration on January 20.

"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," a White House statement said.

The letter also wished the Chinese people a prosperous Lunar New Year of the Rooster, the statement said.

China confirmed it had received the letter on Thursday and said it attached great importance to China-US ties.

At a daily press briefing in Beijing, Chinese Foreign Ministry spokesman Lu Kang said China said cooperation between the two countries was the only option.

Donald Trump upset Beijing by taking a phone call from Taiwan. Credit: AP

Trump and Xi have yet to speak directly although they did talk soon after Trump's presidential election win in November.

The US President upset China in December by taking a phone call from Taiwan President Tsai Ing-wen.

He also threatened to slap tariffs on Chinese imports, accusing the country of stealing US jobs and devaluing the yuan.

But 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".

State Councillor Yang Jiechi told Michael Flynn, Trump's National Security Adviser, last week that China hopes it can work with the US to manage and control disputes and sensitive problems.