Trump wrote the letter to President Xi who had written a congratulatory letter to him soon after he was sworn-in as US President on January 20.
"President Donald J Trump today provided a letter to President Xi Jinping of China, thanking President Xi for his congratulatory letter on the occasion of President Trump's inauguration and wishing the Chinese people a happy Lantern Festival and prosperous Year of the Rooster," White House Press Secretary Sean Spicer said.
In Beijing, a Chinese Foreign Ministry spokesman, reacting to Trump's letter, praised it.
"We highly commend President Trump for expressing festive greetings to President Xi Jinping and the Chinese people," Lu told journalists, adding "cooperation is the only right choice for the two countries."
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After becoming the US President, Trump has spoken with nearly two dozen world leaders, including Prime Minister Narendra Modi. However, Trump has not yet spoken to Xi.
"There is no need for me to comment on this kind of remarks. Interactions between China and US play an irreplaceable role in bilateral ties," Lu said.
British Prime Minister Theresa May was the first world leader to have met him in the Oval Office.
Later this week, Trump would be hosting Japanese Prime Minister Shinzo Abe at the White House. Israeli Prime Minister Benjamin Netanyahu is also scheduled to meet him at the White House.
Trump, after his election, had stated that the 'One- China' policy on Taiwan is up for negotiation and that he is not fully committed to it.
China had hit back saying one-China policy which stipulates that Taiwan is part of Chinese mainland is "non-negotiable". China regards Taiwan as a breakaway province and insist all countries having bilateral ties with it to abide by the 'One-China' policy.