President Donald Trump has sent a letter to Chinese President Xi Jinping, the White House said, weeks after receiving a letter of congratulations from the leader of the Asian giant.

Beijing has been on tenterhooks waiting for a contact from the billionaire president, who seems set to take a hard line against the Asian giant on a wide range of issues from trade to security.

During his campaign, Trump repeatedly attacked Beijing for "stealing" American jobs and has threatened to slap it with massive tariffs.

In his missive, Trump said he looked forward to developing "a constructive relationship that benefits both the United States and China," spokesman Sean Spicer said in a statement Wednesday.

The billionaire politician has already had phone conversations with more than a dozen foreign leaders since he was inaugurated last month.

His decision to send a letter, rather than call the head of the world's second largest economy, could be read as a snub, raising questions about how willing Trump is to engage with a country that he has accused of "raping" the United States.

It is not clear if or when he will dial Xi up.

But Lu Kang, a spokesman for China's Ministry of Foreign Affairs, still praised the letter at a regular press briefing on Thursday.

"We highly commend President Trump for expressing festive greetings to President Xi Jinping and the Chinese people," Lu said, adding "cooperation is the only right choice for the two countries."

Just after winning the November election, Trump provoked Beijing's ire by accepting a congratulatory call from Taiwan's President Tsai Ing-wen.

Washington cut formal diplomatic relations with Taiwan in 1979, recognizing the Communist mainland rulers in Beijing as the sole government of "One China."

Under the terms of the 1979 Taiwan Relations Act, Washington maintains an ambiguous approach to the island, keeping trade ties and selling Taipei weapons.

But the law does not recognize Tsai as a head of state, and China was infuriated at what it saw as a breach of protocol in Trump's acceptance of her call.

In December, Trump told The Wall Street Journal that "everything is on the table, including One China," suggesting that Beijing could save the policy by negotiating a trade deal with him.

In the shadow of this exchange, Chinese officials were anticipating a conciliatory message from Trump, according to Song Guoyou, an expert in China-US relations at Fudan University in Shanghai.

Trump took "a long time to learn the real importance of the volatile relations between China and the US," Song told AFP.

But he said the letter is "a very good sign" that Trump and his team will "take a pragmatic attitude toward China."

In recent weeks, Chinese social media users have expressed indignation at Trump's lack of engagement with Xi, particularly during last week's Lunar New Year holiday.

The outrage was somewhat mollified last Wednesday, when Trump's daughter Ivanka and her Chinese-speaking toddler attended a Lunar Near Year celebration at the Chinese embassy in Washington.