"The two leaders discussed numerous topics and President Trump agreed, at the request of President Xi, to honour our 'One China' policy," the White House said after Trump and Xi spoke over phone.
Xi appreciated Trump's affirmation of One China policy, Chinese state media reported.
Representatives of the US and China will engage in discussions and negotiations on various issues of mutual interest, the White House said.
"The phone call between President Trump and President Xi was extremely cordial, and both leaders extended best wishes to the people of each other's countries," it said, adding that they also extended invitations to meet in their respective countries.
Trump and Xi look forward to further talks with very successful outcomes, the White House said of the "lengthy conversation" the two leaders had.
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 insists all countries having bilateral ties with it to abide by the 'One-China' policy.
Trump has also often accused Beijing of unfair trade practices, currency manipulation and military buildup in the South China Sea.
Earlier in the day, a presidential spokesman said Trump believes that a constructive relationship between China and America is in the fundamental interest of both countries.
"I think it (US-China relationship) is obviously important to us and the President understands that. He has spoken fairly often about China. He understands both the national and economic interests that we have, the desire for our companies to access the Chinese market, but also the national security interests that we have," White House Press Secretary Sean Spicer told reporters at his daily news conference.
Trump, Spicer insisted, wants to have a fruitful and constructive relationship with China.
"And he looks forward to developing that as we go forward," Spicer said.
The phone conversation between the two leaders happened a day after Trump wrote a letter to Xi and on the eve of his scheduled meeting with Japanese Prime Minister Shinzo Abe.
Xi Jinping had sent a congratulatory letter on the day of the President's inauguration.
Trump sent a letter to Xi to wish him and the people of China a happy Lantern Festival.