The president's top economic adviser, Larry Kudlow, said that the talks with Liu He will determine whether a deal can be made by the end of the 90-day detente that Trump and China's Xi Jinping agreed on at the end of the G20 summit.
The United States and China opened a pivotal round of high-level talks on Wednesday aimed at digging out from their months-long trade war amid deep differences over Chinese practices on intellectual property and technology transfer.
"Meetings are going well with good intent and spirit on both sides", he wrote on Twitter Thursday.
Trump added that he and the Chinese representatives were trying to do a complete deal, "leaving NOTHING unresolved on the table".
He said: "All of the many problems are being discussed and will be hopefully resolved".
But the likelihood of reaching a deal before the March 1 deadline set by Trump for the imposition of higher tariffs on Chinese imports is slim.
Trump said any deal must include China opening its market to USA financial institutions, manufacturing and agriculture as well as other unspecified "businesses and industries".
President Donald Trump has said he favors a healthy Chinese economy, but not at the expense of American business and know-how.
Also hanging over the talks is are US indictments against Chinese top telecommunications equipment maker Huawei Technologies Co, accusing it of bank and wire fraud to evade Iran sanctions and conspiring to steal trade secrets from T-Mobile US Inc. But some analysts say that securing an agreement addressing USA complaints about China's alleged theft of trade secrets, forced technology transfer requirements for joint ventures and discrimination against foreign companies is hard to imagine in the short time remaining.
"It can't be settled below that level", William Reinsch, a former Commerce Department official, said of the U.S. 'But it's a very big deal, that would be if it does happen, it would be by far the largest trade deal ever made'. Trump was meeting on Thursday afternoon with the Chinese negotiators.
The White House announced earlier this month that Trump plans to meet in late February with North Korean leader Kim Jong Un.
US officials and some analysts say they believe its weakening economy will pressure the Chinese into making concessions. As part of the standoff between the world's two biggest economies, Washington imposed tariffs on $250 billion in Chinese imports. We're talking about they're going to buy some corn.
Chinese officials have said their policies do not coerce technology transfers.
Chinese officials are resistant to the wholesale changes sought by the United States and the charges against Huawei - one of China's biggest and most successful technology firms - have added to the political tensions. "Rob the American company of its intellectual property, replicate that technology and replace the American company in the Chinese market and, one day, in the global market".
In the spring of 2018, US Treasury Secretary Steven Mnuchin led the US delegation sent to Beijing to advance trade negotiations - but with little success.