China's official Xinhua News Agency said that Xi accepted the call at Trump's invitation.
"China has been hurt over the last number of months. We talked about many subjects, with a heavy emphasis on Trade", Mr Trump tweeted.
The U.S. and Chinese presidents will "certainly" meet at the G-20 summit in Argentina, White House trade adviser Peter Navarro said Friday.
Despite the promise offered by the Trump-Xi telephone call, the level of tension between the two nations was demonstrated just hours after it ended when the U.S. filed charges against Chinese technology firm Fujian Jinhua Integrated Circuit Co and its Taiwanese partner.
The moves also follow media reports that pointed to progress on the US-China trade dispute. Suddenly, talks of 7.00 has nearly all but evaporated and the surge higher in the yuan here will continue to give added backing to gains seen in the aussie and the kiwi ahead of the USA jobs report later.
Tennessee Senator Lamar Alexander told the official the US and China are competitors not adversaries and suggested they can prosper together.
The Trump administration presented Chinese officials with a list of more than 140 demands during the first round of trade talks in May.
The possible warming of relations comes after months of escalating tensions over trade that are threatening to spill into other areas of disagreement, including freedom of navigation in the South China Sea.
Russia, US, Saudi Arabia produce 33% of global oil supplies
Brent crude oil futures were down 34 cents at $77.28 a barrel at 1005 GMT, while US crude futures fell by 30 cents to $67.29. The second round of USA sanctions reimposed by president Donald Trump in May kick in on November 4.
Xi was quoted as saying after the call with Trump that they had hoped to expand trade cooperation.
Trump has also threatened to impose tariffs on all remaining goods imports from China, which past year were worth US$505 billion.
In comments to state media, Xi said he hoped China and the United States would be able to promote a steady and healthy relationship, and that he was willing to meet with Trump in Argentina.
Kudlow believes China is getting isolated in the ongoing trade war, as the United States, Japan, and the European Union officials met in September in NY on the sidelines of the U.N. General Assembly and reached a deal to tackle China's unfair trade practices. "But the tariffs already imposed will not go away", Tu said.
Shi also said he thought China had only a limited role to play on the North Korea issue.
A Justice Department indictment targeted two companies based in China and Taiwan and three individuals, saying they conspired to steal trade secrets from US semiconductor company Micron Technology Inc. Trump said trade talks were "moving along nicely" and that meetings were "being scheduled" at the G20 summit in Buenos Aires.
The United States has imposed tariffs on $250-billion worth of Chinese goods, with duties on $200-billion of the total set to increase to 25 per cent from 10 per cent on January 1, 2019. In response, Beijing said it would impose taxes on 5,207 U.S. imports worth about $60 billion.
One person said a sticking point in any potential deal is intellectual property theft, where the Trump administration has sought to take a hard line.