During the phone conversation, Trump said he fully understands the high significance of the USA government's pursuit of the one-China policy, adding that the US government adheres to the one-China policy.
Chinese officials on Thursday heaped praise on President Trump for sending New Year's salutations to Chinese President Xi Jinping-even if the wishes came in a letter almost two weeks late.
In a statement the White House said the leaders of the world's two largest economies had held a "lengthy" and "extremely cordial" telephone call on Thursday evening in which "numerous topics" were discussed.
The White House statement said the two presidents had "extended invitations to meet in their respective countries" and that officials from both countries would now engage in "discussions and negotiations on various issues of mutual interest".
"I believe that the United States and China are cooperative partners, and through joint efforts we can push bilateral relations to a historic new high", the statement quoted Xi as saying. The two leaders spoke Thursday, and Trump pledged to honor the "One China" policy.
At this moment, writing to Xi and pledging a "constructive" tie with Beijing showcases that stabilizing US-China ties at this hard moment is "of greater significance" for Trump, Yuan said.
Trump said China and the United States are "on the process of getting along very well", which he said will also be very much beneficial to every country in the Asia-Pacific region, including Japan.
"So, I don't want China dictating to me", Trump said.
State-run media in China said Trump had "stressed that he fully understood the great importance for the US government to respect the One China policy", and that "the USA government adheres to the One China policy".
Since 1979, a cornerstone of American-China relations has been the exclusive acknowledgment of the Chinese government.
The President stoked diplomatic concerns after he arranged phone call with Taiwan President Tsai Ing-wen shortly after the 2016 election.
Beijing will not do business with countries that recognise Taiwan diplomatically.
China sees Taiwan as a breakaway province to be reunited with the mainland, by force if necessary.
The phone call to Xi came a day after Trump sent a letter wishing China a "prosperous Year of the Rooster" - which was sent 11 days after China celebrated its Lunar New Year festival. But that all changed with the phone call last night strategically timed during the Chinese new year holiday.
However, this may also be an example of Trump listening to the advice of his cabinet, especially that of Secretary of State Rex Tillerson, who took a markedly different position than Trump on U.S.