"I would really say, and I say it again, a lot of the most hard points that we didn't think we could ever do or we wouldn't agree to, on both sides have been agreed to", he said.
Later in his remarks, Trump said Washington and Beijing have a global responsibility and that a US-China trade deal would be a "tremendous thing for the world".
A final sticking point appears to be when and how Washington will agree to lift the steep tariffs it has placed on more than $250 billion in Chinese imports.
Also unclear is whether China will agree to the Trump administration's demand for an enforcement mechanism allowing the USA to reimpose tariffs if it believes Beijing is not fulfilling its obligations.
US President Donald Trump has in the past threatened to tax all of Chinese goods going into the US.
This could perversely serve to give Chinese state enterprises a greater market role while making USA exporters more reliant on the Chinese government's purchasing decisions - both contrary to Trump's stated goals. Otherwise it would be very tough for us to allow that to happen, ' he added, without elaboration.
World stocks have turned higher ahead of U.S.jobs figures and after U.S. President Donald Trump said talks to ease a trade war with China were making progress.
Mr Trump wants China to buy more American exports and has already won Beijing's assurances it will do so.
Analysts say any agreement is likely to include banner announcements that China has agreed to increase purchases of American commodities like soybeans and fuel.
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Asked about the potential for a meeting between the presidents, China's Foreign Ministry told a news briefing on Thursday that it had noted that Trump had repeatedly expressed his hope to meet with Xi.
Republican Sen. Charles Grassley said the US hopes to complete the trade negotiations by the end of April.
He said no decisions have been made on automobile tariffs.
Kudlow said on Wednesday that United States charges against Chinese telecommunications giant Huawei Technologies Co Ltd had generally not come up during trade talks. China had answered to this by imposing $110 billion worth tariffs on the United States goods.
Addressing the National Republican Congressional Committee spring dinner in Washington on Tuesday, Trump said Xi had denied he was a king.
While some reform pledges by Beijing are largely agreed upon, including an agreement to avoid currency manipulation, the two sides have not yet settled on an enforcement mechanism to ensure that China keeps its pledges.
From the outset, his administration has been divided between advisers who fear the trade war's impact on the economy and financial markets and those who believe a showdown with China is long overdue.
"We've had almost two decades of broken promises from China".