The White House provided no additional information, and in a briefing in Beijing a few hours later, a spokesman for the foreign ministry declined to comment on any changes to auto tariffs.
Beijing has not yet confirmed the move and President Trump's advisers appeared less certain about the agreement.
Trump, who joined Xi in calling a truce on an intensifying trade war between their two powerhouse countries, touted a roll-back in Chinese tariffs on US-made cars.
The White House said talks would take place to resolve within the next 90 days specific US complaints such as forced technology transfer, or else existing 10 percent tariffs would go up to 25 percent.
The White House said Trump and Xi agreed to immediately begin negotiations on structural changes with respect to forced technology transfer, intellectual property protection, non-tariff barriers, cyber intrusions and cyber theft, services and agriculture.
Kudlow didn't provide details on what the White House would to do eliminate or change the electric vehicle tax credits, which would require an act of Congress. Experts doubt the sweetener can be changed by executive order.
Chinese regulators did not respond to requests for comment on Trump's tweet on autos tariffs. These had been scheduled to increase to 25 percent on January 1 but were postponed as part of the weekend agreement.
President Trump is taking a different approach, where he's really stressing his chemistry with President Xi.
The uncertainty underscored the risk entailed by Trump's eagerness to strike deals without nailing down details in advance.
American Apparel & Footwear Association President and CEO Rick Helfenbein said the AAFA is "encouraged" by the news.
"We want to end, we will end those subsidies and others of the Obama administration", Kudlow said.
Senior Chinese officials did not mention this deal in a news conference.
The US president later said in a tweet that Beijing had "agreed to reduce and remove tariffs on cars coming into China from the US". Mnuchin, in an interview with CNBC on Monday, put a US$1.2 trillion price tag on China's additional trade commitments, but emphasized the details of how they get there still need to be negotiated.
His comments relate to the 40% tariff China imposes on United States vehicle imports, which were brought in as part of the trade battle in July. That's added on top of a 15% tariff that Beijing charges for imports from the rest of the world, leaving USA auto exporters facing a 40% levy at the Chinese border.
In a briefing to reporters, he also said the United States did not yet have a "specific agreement" on auto tariffs. Such a change would have to apply to all countries under World Trade Organization rules. "And we know that", Kudlow said.
The United States agreed not to raise tariffs further on January 1, while China agreed to buy more agricultural products from US farmers immediately. "I don't agree with that", he said.