At the close, the Shanghai Composite index was down 0.6 percent at 3,133.72, while the blue-chip CSI300 index also lost 0.6 percent at 3,879.89.
They were off intraday lows as E-Mini futures for the S&P 500 jumped more than 1 percent.
The Wall Street Journal reported US Treasury Secretary Steven Mnuchin and US Trade Representative Robert Lighthizer listed steps that Washington wants China to take in a letter to Liu He, a newly appointed vice premier who oversees China's economy.
China's foreign ministry said on Monday Beijing is willing to hold talks with the United States to resolve their differences in a hopeful sign a potentially damaging trade war could be avoided.
The tech-heavy start-up board ChiNextP jumped 3.2 percent, led by semiconductor companies and biological products makers.
"The China-U.S trade spat could prompt Beijing to push forward with innovation strategy as it puts more focus on the quality of its economy," said Chen Xiaopeng, an analyst with Sealand Securities.
As part of efforts to foster new growth drivers, the Export-Import Bank of China (EximBank) and the country's top economic planner have signed an agreement to boost financing support to emerging industries by more than $100 billion.
For other parts of the stock market, sentiment was still soured by fears of full-blown trade war between the United States and China.
Most sectors fell on Monday, led by financials and energy firms, while gains were seen in few sectors including healthcare companies.