The benchmark S&P 500 surpassed its 50-day moving average, a key indicator for short-term momentum, and is now just 1.76% away from its record high.
Earlier, China's Commerce Ministry said its trade team would lay the groundwork with their US counterparts in mid-September for the October talks, providing relief for markets around the globe that have been bruised by the drawn-out trade war.
Technology stocks provided the biggest boost to S&P 500, rising 1.72%, while financials jumped 1.96%, the most among the 11 major S&P sectors.
Interest rate-sensitive banks surged 2.62%, following a rise in US Treasury yields.
"The trade news was the spark that lit this rally and then the economic data extended it," said Michael Antonelli, market strategist at Robert W. Baird in Milwaukee.
The ADP National Employment Report, considered a precursor to the Labor Department's more comprehensive jobs report, showed US private employers' payrolls grew at the fastest pace in four months in August, led by big gains in service-sector jobs.
At 13:06 ET, the Dow Jones Industrial Average was up 392.12 points, or 1.49%, at 26,747.59, the S&P 500 was up 35.56 points, or 1.21%, at 2,973.34 and the Nasdaq Composite was up 116.06 points, or 1.45%, at 8,092.94.
In deal news, insurer Prudential Financial Inc agreed to acquire online insurance startup Assurance IQ Inc for $2.35 billion. Shares of Prudential fell 2.6%. Among losers were the defensive utilities, real estate and consumer staples sectors.