U.S. Commerce Secretary Wilbur Ross expressed optimism on Monday, telling CNBC that "there's a very good chance that we'll get a reasonable settlement".
China says it is trying to protect its own economic interests and has accused the US of violating global trading rules. The Russell 2000 index of smaller company stocks rose 0.9 percent to 1,438.81.
Six months after Trump first slapped tariffs on Chinese goods, signs are growing that the trade war is exacting an economic and financial cost, increasing the incentive for both sides to end the conflict.
People familiar with the talks said the world's two largest economies were further apart on Chinese structural reforms that the Trump administration is demanding in order to stop alleged theft and forced transfer of U.S. technology and on how to hold Beijing to its promises.
In a statement, the office of U.S. Trade Representative Robert Lighthizer said the two sides considered ways to "achieve fairness, reciprocity and balance in trade relations".
Companies in both the United States and China are feeling the pain from the effects of the U.S. Trump tweeted on Tuesday.
Heightened risk appetite boosted U.S. Treasury yields to the highest this year, while the U.S. dollar extended losses after minutes from a December 18-19 Federal Reserve policy meeting showed many Fed policymakers said the central bank could be patient on future rate hikes. In fact, the two sides may be even further apart on these underlying issues like forced technology transfer and intellectual property protection, among others, according to Bloomberg. Forecasters expect American orders to slump this year.
A senior Chinese official said Beijing plans to introduce policies to boost domestic spending on items such as autos and home appliances this year.
China has also cut tariffs on imports of cars from the United States, dialled back on an industrial development plan known as "Made in China 2025", and told its state refiners to buy more U.S. oil.
USA companies also want action on Chinese policies they complain improperly favor local companies.
Trade talks between China and the United States this week were extensive, and helped establish a foundation for the resolution of each others' concerns, China's commerce ministry said today, but gave no details on the issues at stake.
Trump is also under pressure to reach an agreement amid a United States economic slowdown and high levels of volatility on Wall Street. The 28-nation trade bloc has filed a challenge in the World Trade Organization against Chinese licensing rules it says hinder foreign companies from protecting and profiting from their technologies. "I don't want to comment on what that will look like".
"That's not something that's going to be done by March", he said.
If US crude futures can break through the $55 level, "you're going to see real yields probably lower".
For its part, Beijing is unhappy with US export and investment curbs, such as controls on "dual use" technology with possible military applications. They say China's companies are treated unfairly in national security reviews of proposed corporate acquisitions, though nearly all deals are approved unchanged. China is facing a slowdown in economic growth, in part as a result of falling exports to the US. The US team was led by Deputy US Trade Representative Jeffrey Gerrish, who is reportedly closely aligned to Lighthizer.
Official US fuel storage data from the Energy Information Administration is due at 1800 GMT on Wednesday.