In their first interaction since the U.S. election, Chinese state media said Xi told Trump in a telephone call on Monday that as the world's largest developing and developed economies, there were many areas where China and the United States could cooperate.
"The facts prove that cooperation is the only correct choice for China and the United States," China Central Television (CCTV) cited Xi as saying.
Xi's remarks were a reiteration of phrasing typically used by Beijing to describe bilateral relations.
The two sides must "promote the two countries' economic development and global economic growth" and "push for better development going forward in China-U.S. relations", Xi said.
"During the call, the leaders established a clear sense of mutual respect for one another, and President-elect Trump stated that he believes the two leaders will have one of the strongest relationships for both countries moving forward," a statement from Trump's presidential transition office said.
The two agreed to maintain close communications and meet soon, CCTV said. Xi had congratulated Trump in a message delivered shortly after his surprise election victory last week.
There is intense speculation over the impact of Trump's win on issues facing the two countries, from climate change and global trade to the security balance in the Asia-Pacific.
Trump's criticism of U.S. allies, including Japan, for free-riding on U.S. security guarantees, has deepened anxiety among Washington's allies about its commitment to post-war security arrangements in the face of a rising China and volatile North Korea.
Trump appears to be seeking quick ways to withdraw the United States from a global accord to combat climate change, which has been billed by China and U.S. President Barack Obama as a key area for cooperation.
China has also signalled it will promote plans for regional trade integration, vowing to seek support for a Beijing-backed Asia-Pacific free trade area at a summit in Peru later this month, after Trump's win dashed hopes for the U.S.-led Trans-Pacific Partnership (TPP).
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