The US president has also threatened to extend his punitive tariffs to all Chinese imports if face-to-face talks with Xi, planned for November 29 in Buenos Aires, Argentina, fail to break the deadlock on trade.
The telephone conversation on Thursday was Trump and Xi's first publicly disclosed call in six months.
Dealers were set for a strong end to a healthy week after Mr Trump's tweet, which was a rare sign of hope in the months-long stand-off between the world's top two economies that many fear could batter global growth.
The yuan had come under intense pressure to weaken of late, as slowing growth in China and trade tensions with the USA prompted investors to shift away from riskier emerging-market assets.
In a phone call with U.S. President Donald Trump, Xi also said China would continue to play a constructive role in the process.
But within hours of the upbeat assessments, the US Justice Department took aim at another Chinese firm it accused of unfair practices, part of an across-the-board pressure campaign by the Trump administration targeting China. He has also emphasized the need to reduce the US trade deficit with China.
"It is possible some good positive things could - I say could - come out of President Trump-President Xi talks".
"The economic teams of the two countries should strengthen contact, conduct consultations on issues of mutual concern, and push for a mutually acceptable solution to China-US economic and trade issues", Xi said.
On Thursday Chinese Premier Li Keqiang also told a group of visiting US politicians that China and the United States could overcome their differences and get relations back on track if they worked together in a spirit of mutual respect. 'But we have a chance to make a fair deal, because China has been hurting us and trade deals have been hurting us.
'We talked about many subjects, with a heavy emphasis on Trade.
China and the United States are locked in an increasingly bitter trade war, and both countries have already placed tariffs on some of each others' imports.
Pompeo's comments were the latest slur to come out of Washington, which has accused Beijing of meddling in USA politics, conducting cyber espionage against aviation firms and hacking Trump's iPhone. But Kudlow cautioned that Trump would "aggressively" pursue his agenda against China, if no deals were reached on intellectual property theft, cybersecurity and tariffs on commodities, among other issues.
Tennessee Senator Lamar Alexander told Li that the delegation was there 'to show our respect to a great country and a great people, ' and that the two countries 'are competitors but not adversaries'. And they're having a hard time, and they'll be fine.