Beijing has not yet confirmed the move and President Trump's advisers appeared less certain about the agreement.
Chinese officials discussed the possibility of lowering tariffs on US vehicle imports before Xi met Trump in Argentina, according to a person familiar with the situation who asked not to be identified.
Senior Chinese officials did not mention this deal in a news conference.
Stocks fell following Trump's tweetstorm with the Dow Jones industrial average declining almost 3%.
The clock started ticking on December 1, when Trump met in Buenos Aires with China's leader Xi Jinping and agreed to work towards an agreement to roll back the exchange of tariffs on hundreds of billions of dollars in two-way trade. But if not remember, I am a Tariff Man", he tweeted on Tuesday. "When people or countries come in to raid the great wealth of our Nation, I want them to pay for the privilege of doing so.
Trump's economic team has spun his knee-jerk protectionism as a tactic created to negotiate "better" trade deals - but so far, those better trade deals don't seem to be stronger than the status quo ante.
Markets took a dive following Trump's tweetstorm.
The Dow Jones Industrial Average .DJI fell more than 3 percent, the S&P 500 .SPX lost 3.2 percent and the Nasdaq Composite .IXIC tumbled 3.8 percent.
Some industry participants expected China to drop the tariffs soon after the Trump-Xi meeting. It also said China has agreed to start purchasing agricultural products from U.S. farmers immediately.
A lack of detail from the Chinese side has left investors and analysts wondering if Mr Trump's exuberance is warranted, and if details touted by the White House but left out of Chinese reporting on the agreement are in question.
Cui added that negotiators would actually have less than 90 days to reach a deal because of holidays in both countries over the next three months.
Trump agreed he will leave the tariffs on $200 billion worth of Chinese products at 10 percent, and not raise it to 25 percent as he has threatened to do January 1, according to a White House statement. The Chinese Foreign Ministry says Trump and President Xi "reached consensus not to impose new additional tariffs and agreed to instruct the economic teams of the two sides to step up negotiations toward the removal of all additional tariffs"-closer to Trump's claim, but nowhere near as certain".
The appointment of Lighthizer, the hardline United States trade representative, to lead the talks instead of Treasury Secretary Mnuchin puts one of the administration's toughest China critics in charge. U.S. Treasury Secretary Steven Mnuchin has made it clear there's only one person leading the trade negotiations with China. He noted that the talks would be finalized within 90 days after his meeting with President Xi Jinping at the G20 forum.
"The window of doing bean business to China is getting really skinny, nearly to the point where it is closed", said Roy Huckabay, of Linn and Associates, a Chicago brokerage.
This was also the first time that the president suggested the negotiating window could be extended.
"But if a fair deal is able to be made with China, one that does all of the many things we know must be finally done, I will happily sign", Trump said.
However, Trump held out the possibility of an extension.