The letter was read out by a member of the Chinese delegation before Trump in his Oval Office of the White House in front of a battery of reporters.
Xi is pleased that the economic teams have engaged in intensive consultations and made significant progress, according to the letter.
Trump and Xi had a dinner summit in Buenos Aires on December 1 last year. Top trade officials from the two countries have so far met several times.
This has been well received in both our countries and in the wider international community. It is my hope that our two sides will continue to work together in the spirit of mutual respect and win-win cooperation, and could redouble our efforts so as to meet each other halfway and reach an agreement that works for our mutual benefit, said the Chinese President.
In his letter, Xi mentioned about the letter and a video that he received from Trump earlier.
Not too long ago, you sent to me a special letter of festive greetings, together with the lovely video made for me and my wife by your grandchildren on the Chinese Lunar New Year.
We enjoyed the performance greatly and were happy to see that the little ones have kept improving in their Chinese. We watched the video more than once and feel that we must for these adorable grandchildren of yours, Xi said.
Trump told reporters that the video he's talking about is a video made by his daughter Ivanka and son-in-law Jared Kushner, and their children speak fluent Chinese, even though they're very young.
They were taught, at a very young age, Chinese. And when President Xi met Arabella, who's the oldest (daughter of Ivanka Trump), he said this was like perfect Chinese at the time I thought that was nice. And they actually made a little video that they sent to President Xi.
I thought it was a very nice thing. And it shows a great friendship between the two countries. And that was really just a Happy New Year' wish that was given in Chinese by Arabella -- mostly by Arabella and her two brothers, the US President added.
Top trade officials from America and China are currently holding talks in the US to negotiate a comprehensive trade deal before their self-imposed deadline of March 1.