The two economic superpowers have already imposed duties on more than US$360 billion in two-way trade, which has weighed on their manufacturing sectors and shaken global financial markets.
Mr Mnuchin is heading the U.S. delegation along with trade representative Robert Lighter and the pair are expected to meet China's vice premier Liu He in Beijing tomorrow and Friday.
"Looking forward to discussions today", Mnuchin was quoted by Reuters as saying, without elaborating, as he left his hotel on Thursday morning. But they also believe China's goal is to make enough progress to persuade Mr. Trump to extend his deadline.
Chinese officials also are balking at US pressure to accept an enforcement mechanism to monitor whether Beijing carries out its promises, said Kuijs.
Trump also has said he expects to meet with Xi "at some point" to clinch a trade deal.
"So far, so good", he said when asked by reporters on how the meetings in Beijing went. "They're showing us tremendous respect".
US Department of Agriculture Deputy Secretary Stephen Censky said on Wednesday that the two presidents were expected to meet "sometime in March", but no dates were set.
"Markets will continue to watch - and react - closely to the ups and downs of the negotiations", said Trey McArver of Trivium Research.
Negotiators have said any final agreement will have to be made by Mr. Trump and his Chinese counterpart, Xi Jinping.
The two days of talks starting Thursday allow too little time to resolve the war over Beijing's technology ambitions that threatens to drag on weakening global economic growth, businesspeople and economists say.
Washington is demanding far-reaching changes to Chinese practices that it says are unfair, including theft of United States technology and intellectual property, and myriad barriers that foreign companies face in the Chinese domestic market.
Beijing has offered to boost its purchases of USA goods but is widely expected to resist calls for major changes to its industrial policies such as slashing government subsidies.
The Chinese government has offered few details about the state of negotiations this week.
US Treasury secretary Steven Mnuchin told reporters in the Chinese capital that talks were going well.
China's imports, however, continued to fall in January, down 1.5 percent from a year earlier, though at a slower pace than a 10.2 percent decline forecast by Bloomberg News. While down from the record peak late previous year, China still had a $27.3 billion trade surplus in goods with the U.S.in January, according to data released on Thursday in Beijing.
A growing number of U.S. businesses and lawmakers have expressed hopes for a delay in the tariff increase while the two sides tackle the hard USA demands for major structural policy changes by China.
But China has denied accusations of trade abuses.
Trump met with Liu at the White House when a Chinese delegation came to Washington for talks at the end of January.
The state-run tabloid Global Times said in an editorial late on Wednesday that although Washington had started the trade war, it "was now more willing to reach an agreement".