US stocks rallied on hopes that the two countries might lower the steep trade barriers they have erected over the past month, though there was no sign that negotiations might start anytime soon.
Bessent said the tariffs - 145 per cent on Chinese products and 125 per cent on US products - would have to come down before trade talks can proceed, but said Trump would not make that move unilaterally.
"Neither side believes that these are sustainable levels. As I said yesterday, this is the equivalent of an embargo and a break between the two countries in trade does not suit anyone's interest," Bessent told reporters on Wednesday.
The White House is open to discussing a significant rate cut on Chinese imports in order to advance negotiations with Beijing but will not do so alone, according to a person familiar with the conversations.
That person would not say how low the White House might be willing to go, but the Wall Street Journal reported the figure could be as low as 50 per cent.
A White House spokesperson dismissed any reports as "pure speculation," and said news on tariffs would come from Trump himself.
"We are going to have a fair deal with China," Trump told reporters, but did not outline any specifics.
The tariff levels outlined in the Journal report would likely still be high enough to deter a significant chunk of trade between the world's two largest economies. German shipper Hapag-Lloyd said Wednesday that 30 per cent of its US-bound shipments from China have been cancelled.
Separate talks between the two countries over tackling the fentanyl epidemic have not yielded results so far, sources say.
The apparent US softening on China tariffs was a welcome sign for markets battered by Trump's erratic trade policies. The benchmark S&P 500 finished the day 1.67 per cent higher at 5,375.86, but is still more than 12 per cent below its February record close.
"It's about all of the political and policy uncertainty and what it could mean for the economy in the near term," said Jim Baird of Plante Moran Financial Advisors.
Bessent said the third quarter of this year is a "reasonable estimate" for achieving clarity on the ultimate level of Trump's tariffs.
In addition to the steep tariffs on China, Trump has also imposed a blanket 10 per cent tariff on all other US imports and higher duties on steel, aluminium and autos.
He has suspended targeted tariffs on dozens of other countries until July 9 and floated additional industry-specific levies on pharmaceuticals and semiconductors. That has roiled financial markets and raised fears of recession.
The European Union, which Trump has threatened with 20 per cent tariffs, would respond with counter-tariffs if it cannot reach a deal before the July 9 deadline, economy minister Valdis Dombrovskis said on Wednesday.
Other countries are looking to negotiate as well. Vietnam's trade minister spoke to US Trade Representative Jamieson Greer on Wednesday, state media reported.
Twelve US states have filed suit against the Trump administration on Wednesday in the US Court of International Trade claiming that tariffs established through the International Emergency Economic Powers Act are illegal. They joined California, which filed a separate suit against the government last week, in challenging the tariffs.
The International Monetary Fund said Wednesday the tariffs will slow growth and push debt higher across the globe. S&P Global found that US business activity slowed to a 16-month low in April while prices charged for goods and services soared.
The Federal Reserve said it found economic activity in the United States to be steady over the past month, despite "pervasive" uncertainty around trade.
A Reuters/Ipsos poll found Americans souring on Trump's economic performance. Just 37 per cent of respondents approve of his handling of the economy, down from 42 per cent when he took office in January.
