The Dow Jones Industrial Average rose 113.37 points, or 0.40 percent, to 28,308.79. The S&P 500 was up 16.20 points, or 0.47 percent, to 3,443.12. The Nasdaq Composite Index increased 37.61 points, or 0.33 percent, to 11,516.49.
Ten of the 11 primary S&P 500 sectors advanced, with energy closing up 1.13 percent, leading the gainers. Consumer staples dipped 0.11 percent, the lone declining group.
U.S.-listed Chinese companies traded mostly higher, with nine of the top 10 stocks by weight in the S&P U.S. Listed China 50 index ending the day on an upbeat note.
U.S. House Speaker Nancy Pelosi and Treasury Secretary Steven Mnuchin "continued to narrow their differences" on the next round of COVID-19 relief package in a call on Monday, and they were slated to speak again on Tuesday, according to Drew Hammill, Pelosi's spokesman and deputy chief of staff.
On Sunday, Pelosi said that the White House and congressional lawmakers must reach an agreement in 48 hours if they want to pass a new COVID-19 relief package before the presidential election in November.
Stimulus negotiations have been a major focus for investors recently as they hoped a follow-up aid package would help combat the economic effects caused by the COVID-19 pandemic.
More than 8.25 million COVID-19 cases have been reported in the United States with deaths over 220,000 as of Tuesday afternoon, showed a tally by Johns Hopkins University.
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