The two countries already have imposed tariffs on hundreds of billions of dollars of each other's goods and Trump has threatened to slap tariffs on the remainder of China's $500 billion-plus exports to the United States if the disputes can not be resolved.
Trump made no mention of whether the two leaders talked about the US indictment unveiled Thursday of two companies based in China and Taiwan accusing them of stealing trade secrets from a USA semiconductor company, Micron Technology Inc.
Mr Trump has asked key U.S. officials to begin drafting potential terms, according to the report.
The two leaders had a telephone call on Thursday, which Trump described as "long and very good", and said in a tweet that their discussions on trade were "moving along nicely". At a campaign rally in Columbia, Missouri, on Thursday night he said, "they want to make a deal". "Also had good discussion on North Korea!"
Trump asked key cabinet secretaries to have their staff draw up a potential deal to signal a ceasefire in an escalating trade conflict, the people said, adding that multiple agencies are involved in the drafting of the plan. Trump said trade talks were "moving along nicely" and that meetings were "being scheduled" at the G20 summit in Buenos Aires.
Asian stocks rose sharply on Friday on hopes of a trade deal between the United States and China.
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However, there is little detail about why they were in New York City and whether they have been there since late August. Police released a sketch of the two women found laying on rocks near the Hudson River off of Riverside Park.
Xander Schauffele, Cameron Champ, Nelly Korda win
Finau was at 13-under 203 and led by three over Justin Rose , Masters champion Patrick Reed and Xander Schauffele . He ended up missing a 20-foot birdie putt; Schauffele hit the green in two shots and made a two-putt birdie.
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Sanders said Trump "cherishes the American Jewish community for everything it stands for and contributes to our country". He noted that his outlet was sent mail bombs in the past week.
Meanwhile, Chinese stocks have been under pressure this year amid trade conerns and slowing domestic economy.
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.
Officials are working to resolve differences ahead of upcoming talks between President Trump and his Chinese counterpart Xi Jinping.
Federal Bureau of Investigation director Christopher Wray said the US has filed a civil lawsuit seeking to prevent the two indicted companies, Taiwan-based United Microelectronics Corp. and China's state-owned Fujian Jinhua Integrated Circuit, from exporting any products created using USA trade secrets and blocking the further transfer of trade secrets.
Just after the upbeat readouts of the Trump-Xi call, the Justice Department announced the latest in a long list of actions against what Trump administration calls China's cheating through intellectual property theft, unfair corporate subsidies and rules hampering U.S. corporations in China. "I don't think they're ready yet".
"While we are still cautious over a full resolution of recent tensions in the medium term, resumption of dialogue between Washington and Beijing would be good enough to investors for now", he told Bloomberg.