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.
While investors have anxious over the trade war between the world's two biggest economies, relations have thawed since Xi and Trump struck a 90-day trade truce in early December while the two sides work to ease tensions by March 1.
In his message to Trump, Xi said that China-US relations have experienced ups and downs, but have made historic progress over the past four decades, China's Xinhua news agency said.
Trump also praised the direction of talks with Beijing, writing on Twitter that "the deal is moving along very well".
Foreign Ministry spokesman Lu Kang said last week that in developing China-US relations, the two sides should view each other's strategic intentions in a rational and objective manner, step up strategic communication, enhance strategic mutual trust and avoid misjudgment.
The US imposed tariffs on a number of Chinese products, including consumer and industrial items such as handbags and rice.
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China recently marked the anniversary of the momentous policy shift agreed at a Communist Party gathering on December 18, 1978 under late paramount leader Deng, who is considered the architect of the country's opening up to the world.
This had brought huge benefits to both nations' people and contributed greatly to world peace, stability and prosperity, Xi said.
But he also stressed China's capacity to weather the storm, citing a series of industrial and technological achievements past year. He said that the government would keep growth from slowing too quickly and follow through on a tax cut as part of an effort "to ease the burden on enterprises".
"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".
Xi also praised the fast development of several of the country's economic zones, such as the Jing-Jin-Ji urbanised region in the north, the Yangtze River economic belt in the east and the Guangdong-Hong Kong-Macau Great Bay Area in the south. China's factories slid back into contraction territory in December, with the manufacturing purchasing mangers index dropping to 49.4.
The U.S. formally established ties with the People's Republic of China on January 1, 1979, cementing a rapprochement that began seven years earlier with President Richard Nixon's landmark visit to Beijing. "Our people are the country's solid foundation and our main source of confidence to govern", Mr Xi said.
The risks confronting investors have market strategists along Wall Street forecasting another turbulent year for stocks in 2019, and potentially one of the most hard years for investors since the bull market began.