By Xie Yu

International markets made small gains, while U.S. stock futures declined, as investors weighed signs of economic recovery against risks stemming from U.S.-China tensions, the new coronavirus and social unrest in the U.S.

By early afternoon Tuesday in Hong Kong, the city's Hang Seng Index and stock benchmarks in Japan and South Korea had all risen 0.5% to 1.5%. China's Shanghai Composite added 0.1%, and Australia's S&P/ASX 200 rose 0.3%.

E-mini S&P 500 futures lost 0.2%.

"The equity market has been pricing in a smooth recovery of the economy, although it might be too optimistic while overlooking some potential risks," said Anthony Chan, chief Asia investment strategist at Union Bancaire Privée.

Among other risks, Mr. Chan cited the possibility of fresh coronavirus outbreaks, bringing new lockdowns, and a fragile geopolitical backdrop. He said the Trump administration could take more-severe measures related to Hong Kong ahead of the U.S. presidential election in November.

In currency markets, the Australian dollar continued to recover from the troughs it hit in mid-March, buying more than 68 U.S. cents for the first time since late January. It stood at 68.05 U.S. cents by early afternoon Hong Kong time.

On Tuesday, the Reserve Bank of Australia left its benchmark interest rate unchanged at 0.25%. Gov. Philip Lowe said the country's downturn could be shallower than expected, although the outlook remained highly uncertain. The central bank's board didn't discuss negative interest rates at its meeting.

The U.S. dollar has slid in recent sessions, and riskier currencies such as the Mexican peso have strengthened, on optimism about economic recovery. On Tuesday morning in Hong Kong, the WSJ Dollar Index, which measures the U.S. currency against 16 others, was fractionally stronger at 92.06. It peaked above 97 in March.

U.S. indexes rose Monday as investors embraced signs that global factory activity was on a path toward recovery and largely shrugged off violent protests in U.S. cities.

In bond markets, the yield on the 10-year U.S. Treasury note eased to 0.658%, according to Tradeweb, down from 0.662% on Monday.

Brent crude, the global oil benchmark, gained 1.1% to $38.74 a barrel.

An alliance of oil-producing nations led by Saudi Arabia and Russia is close to a deal that would extend their collective production cuts through Sept. 1.

Write to Xie Yu at Yu.Xie@wsj.com