Trump has long threatened to impose tariffs on all $500 billion-plus goods that the United States imports from China if Beijing fails to meet his demands for sweeping changes to its policies on intellectual property, technology transfers, industrial subsidies and local market access.
Reports earlier Friday said that President Trump had asked officials to prepare a draft of a trade agreement with the world's second largest economy, prompting the Dow to rise.
"If a Trump-Xi deal at the G20 Summit can set the broad framework for renewed bilateral trade negotiations, it may help the global trading system avert the abyss of an escalating US-China trade war in 2019", said Rajiv Biswas, Asia Pacific chief economist at IHS Markit in Singapore.
Meanwhile in an interview, Secretary of State Mike Pompeo said China was the most important long-term strategic challenge for the US. At a campaign rally in Columbia, Missouri, he later said "they want to make a deal".
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Peter Navarro, director of the National Trade Council within the White House, struck a similar wait-and-see note on Saturday about the Trump-Xi meeting.
"Dollar moderation, the stabilising trade relationship between U.S. and China and more stimulus from Beijing will be the key ingredients to revive market confidence in Asia".
The yuan is continuing to push forward with gains against the greenback as talks of a US-China trade resolution continues to fuel the rally seen in the past two days.
President Trump's comments came a day after a phone call with President Xi that he described as "very good".
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"The Trump administration should not miscalculate China's tolerance for what they perceive as bullying tactics", he said.
Xi was quoted by CCTV as saying after the call with Trump that the two leaders had hoped to expand trade cooperation.
The news comes as the volatile trade relations weigh in on the United States stock market, with stocks taking a turn after a rally in world equity markets came to a close and gains reversed on Wall Street.
The United States has already imposed tariffs on $250 billion worth of Chinese goods, and China has responded with retaliatory duties on $110 billion worth of US goods.
"China very much wants to make a deal... We talked about many subjects, with a heavy emphasis on Trade", Trump tweeted. America's trade deficit with China hit a record high in September, according to figures reported Friday by the U.S. Commerce Department. They also agreed to meet on the sidelines of the Group of 20 summit meeting in Buenos Aires, Argentina, at the end of the month.
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