Trump also revived questions Friday about the location for signing any deal with his Chinese counterpart Xi Jinping.
However, the plan faces stiff internal opposition in the USA administration, Reuters reported on Thursday, and us officials have signaled opposing views on the status of talks.
USA stocks dipped after Trump's comments, made to reporters before he left the White House, and the dollar to fell against the yen.
"I can not get ahead of the talks with China, but we are very, very optimistic that we will reach a deal soon", she said. On Thursday, Kudlow confirmed the Chinese Commerce Ministry's claim of a tariff accord, telling Bloomberg: "If there's a Phase 1 trade deal, there are going to be tariff agreements and concessions".
Stocks soared Thursday after the Chinese government said Beijing and the Trump administration had agreed to remove some tariffs as part of any deal.
Worries the pact could fall apart as there was still no specific agreement for a phased rollback prompted some investors to sell heading into the weekend. Based on talks in October, it would also include $40 billion to $50 billion in Chinese purchases of US agricultural goods and certain currency measures and expanded protections for intellectual property in China demanded by the United States.
U.S. West Texas Intermediate (WTI) crude CLc1 was down 56 cents, or 0.9%, at $61.73 a barrel.
"The question right now is what the two sides have actually agreed on - the market's focus has shifted to how the United States may react to China's tariff remarks tonight or in coming days", Oversea-Chinese Banking Corp Ltd (華僑銀行) economist Tommy Xie (謝東明) said.
If confirmed by the US, such an understanding could help provide a road-map to a deal de-escalating the trade war that's cast a shadow over the world economy.
The US and China agreed to roll back a number of tariffs as part of an attempt to form a trade deal, according to Chinese Commerce Ministry spokesperson, Gao Feng. But the administration's trade adviser Peter Navarro denied talks had reached that stage.
A source briefed on the talks told Reuters on Tuesday that Chinese negotiators want Washington to drop 15% tariffs on about $125 billion worth of Chinese goods that went into effect on September 1.
One possible location was London, where the leaders could meet after a North Atlantic Treaty Organisation summit that Trump is due to attend on December 3-4, the official said.
More complicated issues would be tackled in later negotiations, Ross said.
But China was also seeking cancellation of other USA tariffs put in place since July 2018.