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 programs.
They hope it will lead to more streamlined decision making and see benefits in having an interlocutor who can afford to take some risks domestically.
A senior aide to Trump said "the president has a very good working relationship with Xi Jinping. He wants to continue building on what the president terms a constructive and results-oriented relationship."
"The 19th Party Congress provides the opportunity for us to get some things done in the relationship to put us on a good footing deep into the future."
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