Mnuchin, asked by reporters as he left his Beijing hotel what his hopes were for the visit, said "productive meetings".
The US has said it will increase tariff rates on $200bn worth of Chinese imports from 10% to 25% if the two sides don't strike a deal by 1 March. He did not elaborate.
U.S. President Donald Trump signaled Tuesday he is open to postponing a trade deadline with China if negotiators make sufficient progress on a deal.
The fact that a presidential-level meeting is still in the cards - and that both sides are now reportedly angling for it to happen in mid-to-late March - means that the 90 days of trade talks are likely to be extended past the March 2 deadline. While those purchases will provide relief to US farmers, there has been no breakthrough on the structural issues separating the two nations, such as industrial policy, government subsidies, protection of intellectual property or forced transfers of technology. And so far, I've said don't do that.
Mnuchin, along with U.S. Trade Representative Robert Lighthizer, arrived in the Chinese capital on Tuesday.
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One source who had been briefed on the arrangements noted: "Xi is scheduled to meet both Lighthizer and Mnuchin on Friday". A round of talks at the end of January ended with some progress reported - but no deal and U.S. declarations that much more work was needed.
Negotiators from the two countries are meeting this week in Beijing, with USA officials pressing China to commit to deeper reforms to a state-driven economic model that they say hurts American companies.
U.S. Secretary of State Mike Pompeo cautioned allies on Monday against deploying equipment from Chinese telecoms giant Huawei on their soil, saying it would make it more hard for Washington to "partner alongside them".
Facing an economic slowdown at home, the Chinese government has a strong motivation to address American demands and put an end to the trade war.