"History has proved that cooperation is the best choice for both sides", he said.
China's foreign ministry said in a statement Sunday that Beijing is willing to work with the United States through "storms" in their relationship toward the goal of global stability.
Trump said in a Twitter message Saturday that his phone call with Xi was "long and very good" amid a 90-day truce between the two countries over their trade war.
Da Wei, director of the Center for International Strategy and Security Studies at the University of International Relations, said a basic lesson drawn from the 40 years of China-US relations is that the two countries have better ties when they observe things from a strategic height and with a historical perspective.
Trump said in his congratulatory message that he prioritized promoting cooperative and constructive US-China relations, adding that his solid friendship with Xi has laid a firm foundation to help the two countries see great achievements in the coming years.
The Trump administration also hopes that these negotiations lead to an opening of the Chinese market to U.S. agricultural and manufactured products.
Trade relation between Washington and Beijing is going to improve.
In early January, a USA trade team is expected to visit China to hold a vice-ministerial-level meeting, but a diplomatic source said that it is "very unlikely" that the United States and China will finalize their trade negotiations within 2019.
A standstill agreement reached between Trump and Xi on the margins of the G20 summit in Buenos Aires in November 30 and December 1 deferred the imposition of tit-for-tat tariffs by the two countries till March 1 to allow for negotiations.
But he also stressed China's capacity to weather the storm, citing a series of industrial and technological achievements past year.
"Despite all sorts of risks and challenges, we pushed our economy towards high-quality development, sped up the replacement of the old drivers of growth, and kept the major economic indicators within a reasonable range".
Relations between the world's top two economies are "now in a vital stage", Xinhua quoted Xi as saying during the Trump call. "Our people are the country's solid foundation and our main source of confidence to govern", he said.
The White House says the tariffs are a response to China's unfair trade policies, which Mr Trump blames for helping to create a huge trade deficit.
China's growth is still slowing as it transitions from a high-growth, export-led model to a consumer-focused state.