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Futures tied to the S&P 500 rose 0.5%, suggesting the benchmark index will open higher after advancing for the seventh day running on Monday,its longest winning streak in over a year. Overseas, the Stoxx Europe 600 rose 0.9%, lifted by shares in travel-and-leisure companies and other sectors that are sensitive to the direction of the economy.
Trading has eased this month, leading to some outsize market moves. Through Monday, about 4.4 billion shares had changed hands on the New York Stock Exchange each trading day in August, almost a fifth lower than the average for the year as a whole, according to Dow Jones Market Data.
A key measure of turbulence in American stocks, the Cboe Volatility Index, has also dropped to its lowest level since late February.
Investor sentiment was boosted by signs that President Trump and Democrats are open to restarting negotiations on a broad economic relief package. Administration officials and Democratic leaders urged each other to return to the negotiating table after Mr. Trump issued executive actions on jobless aid and other relief over the weekend.
“The U.S. fiscal stimulus is absolutely critical to keeping market momentum positive,” said Nicholas Brooks, head of economic and investment research at Intermediate Capital Group. “Markets are assuming that ultimately Congress will come through with a package, and that there’s a lot of brinkmanship going on.”
“If we don’t get a deal, I think markets will correct quite quickly,” Mr. Brooks said.
Mr. Trump also said Monday evening that he was “very seriously” considering a cut to capital-gains tax and paring taxes for middle-income families.
“It’s not clear whether he’ll get what he wants,” said Mr. Brooks. “But just the mention of that has I think also increased equity market sentiment overnight.”
New coronavirus cases continued to decline. The U.S. reported fewer than 50,000 new cases for the second day in a row Monday, pushing the total number close to 5.1 million, according to Johns Hopkins University.
However, investors are concerned by a pickup in infections in parts of Europe that had appeared to bring the virus under control.
“It’s hard for markets to digest the conflicting newsflow,” said Hugh Gimber, global market strategist at J.P. Morgan Asset Management. “The news in the U.S. has clearly improved. The news in some parts of continental Europe has deteriorated at the same time.”
One positive for the world economy is that local lockdown measures “have had a less striking impact on mobility and spending data than the much more stringent lockdowns earlier in the year,” Mr. Gimber added.
Companies including food-distributor Sysco and corporate-services firm Broadridge Financial Solutions are due to report earnings before the opening bell in New York. Of the 91% of companies on the S&P 500 that had reported by Monday, 82% had beaten analysts’ profit forecasts, according to FactSet.
In a sign that investors are embracing riskier assets, yields on 10-year U.S. Treasury notes rose to 0.581%, from 0.573% Monday. Yields rise as bond prices fall.
The price of gold,seen as a haven asset by many investors,fell 1.8% to $2,003.50 a troy ounce. Brent-crude futures, the benchmark in international oil markets, rose 0.7% to $45.32 a barrel.
Hong Kong’s Hang Seng Index snapped three days of losses to rise 2.1% by the close of trading. The increase was driven partly by a rally in shares of Macau casino stocks, which jumped after the semiautonomous territory’s government eased quarantine requirements for visitors from mainland China. Authorities also said Macau would soon start issuing visas again, at first to individuals from neighboring Zhuhai. Sands China shares jumped 9.8%, while Galaxy Entertainment Group rose 5.5%.
“The resumption of tourist-visa issuance is a very good sign that rekindled hope among some investors that gaming revenue could be brought back,” said Nate Deng, lodging and tourism analyst at China Renaissance Securities.
Elsewhere, Japan’s Nikkei 225 gained 1.9% while the Shanghai Composite Index lost 1.2%.
—Frances Yoon and Xie Yu contributed to this article.
Write to Joe Wallace at Joe.Wallace@wsj.com