Xu Jinli, who is now working in Russian Federation, represents the China Council for the Promotion of International Trade.
Xinhua, in a commentary, said it was only natural the two countries would have disagreements and encounter problems, considering their "different social systems, development paths and historical and cultural backgrounds".
Trump sent his own congratulatory message in return, saying it was his priority to promote cooperative and constructive US-China relations, Xinhua added.
U.S. President Donald Trump takes part in a welcoming ceremony with China's President Xi Jinping at the Great Hall of the People in Beijing, China, on November 9, 2017.
A day before, on Sunday, US President Donald Trump tweeted that he and Chinese leader Xi Jinping had made "big progress" in a telephone conversation about trade and that a deal was "moving along very well".
Trade officials from the two countries are set to resume talks in early 2019, the 40th anniversary of the United States and China establishing diplomatic ties.
Since the two leaders agreed on a truce on the sidelines of the G20 summit meeting in Buenos Aires, however, there have been small signs of progress - and an absence of new threats from Trump.
The two countries are the world's largest trade partners.
China's President Xi Jinping (L) and US President Donald Trump discussed the tariff war on more than $300 billion worth of goods.
In Saturday's tweet, the United States president said "talks were moving along very well".
"Across the nation, the American people are growing in vigilance, with a newfound appreciation for our administration's actions and the president's leadership to reset America's economic and strategic relationship with China", Pence added.
Meanwhile, a USA delegation led by Deputy Trade Representative Jeffrey Gerrish was preparing for talks in Beijing next week that would test a tariff cease-fire established earlier in the month by the two sides. If no agreement is reached, the USA said it will boost tariffs on $200 billion of Chinese goods to 25% from the current 10%, potentially having a big impact on electronics, furniture, machinery and other US industries that rely on Chinese imports.
But Washington warned at the time that "if at the end of this period of time, the parties are unable to reach an agreement, the 10 percent tariffs will be raised to 25 percent", indicating that a failure to finish negotiations will rekindle trade strains.
Just days after the trade truce was brokered, Trump warned in a December 4 tweet that both national leaders "want this deal to happen", but that if a deal doesn't happen, "I am a tariff man".
Trump says the agreement will be very comprehensive and will cover "points of dispute".
Moscow open for dialogue: Putin to Trump in New Year letter
The recipients included Syrian President Bashar al-Assad, whom Putin has backed throughout a civil war that started in 2011. Putin noted that the efforts of both countries contribute to anti-terror fight and political process in Syria.