A senior administration official told AFP the pair had spoken by telephone after Xi was formally handed a second term.
The congress also saw the Chinese leader fuel speculation about how long he will remain in the post by not anointing a possible successor to take over in five years’ time.
China’s state-run news agency Xinhua reported that Xi expressed a desire to work with Trump to “jointly blueprint future development of China-US ties.”
Trump is expected to meet the Chinese leader during a state visit to China early next month.
That is part of a broader Asia trip likely to be dominated by concerns about North Korea’s ballistic and nuclear programmes.