Trump said trade talks were "moving along nicely" and that meetings were "being scheduled" at the G20 summit planned in Buenos Aires at the end of this month.
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.
"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.
Tennessee Senator Lamar Alexander told the official the US and China are competitors not adversaries and suggested they can prosper together.
"President Xi Jinping also stressed that China-U.S. trade has always been serving as ballast and a stabilizer for China-U.S. relations".
China has been hurt over the past months and is having a "hard time" due to strong steps taken by the USA against it over trade, USA president Donald Trump has claimed.
Stock markets in China gained on Friday after US President Donald Trump said trade talks with Beijing were "moving along nicely".
Trump has imposed penalty tariffs of up to 25 percent on $250 billion of Chinese goods in a dispute over Beijing's plans for state-led development of technology industries.
USA indicts Chinese, Taiwan firms for targeting Micron trade secrets
Donald Trump has slapped tariffs on $250bn in Chinese products in an effort to narrow the U.S. trade deficit with China. It is time for China to join the community of lawful nations". "Our wish is to have a trusted partner".
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.
"We do hope that China and the United States will meet each other halfway and work together in the spirit of mutual respect and equality", Li told Trump's fellow Republicans.
Tennessee Senator Lamar Alexander told Li that the delegation was there "to show our respect to a great country and a great people".
"Both leaders attach great importance to China-U.S. ties and economic ties", Lu said.
"China has been hurt over the last number of months". And they're having a hard time, and they'll be fine, ' Trump said Wednesday.
"The West feels comfortable that some kind of trade deal will get done, and that Xi will support the private sector", said Andy Wester, senior investment analyst at Proficio Capital Partners.
"We are changing them".
Trump warned that if China doesn't "treat us fairly, we're not going to treat them fairly" in remarks at an event for American workers at the White House.