By Xie Yu

Asian stock markets fell, after a third straight session of declines in New York, but futures suggested U.S. equities might regain some poise, and European stocks rose.

Stock futures linked to the S&P 500 added 0.6% Wednesday. European benchmarks rose in early trading, with the pan-continental Stoxx Europe 600 up 0.5% and gains led by Germany's DAX and the U.K.'s FTSE 100.

However, in Hong Kong, the city's Hang Seng Index and China's Shanghai Composite both fell 1.1%. Equity benchmarks in Australia, Japan and South Korea dropped 2.5%, 1.4% and 0.7% respectively.

Falls in big technology stocks pushed the Nasdaq Composite Index down 4.1% Tuesday. That took its losses over three sessions to 10.03%, pushing it into correction territory.

"The correction in the U.S. market really weighed on sentiment here," said Ken Wong, a portfolio manager at Eastspring Investments in Hong Kong. Still, Mr. Wong said the pullback shouldn't have come as too much of a surprise, given some stocks had doubled or tripled in value in a few months.

In Hong Kong, shares in Meituan Dianping, the operator of one of China's biggest food-delivery apps, fell 3.3%, extending a recent reversal after huge gains earlier this year. Games and messaging giant Tencent lost 0.9%, while smartphone maker Xiaomi dropped 1.3%. Japan's SoftBank Group dropped 4%, while Taiwan Semiconductor Manufacturing Co. shed 1%.

Falling oil prices were also curbing risk appetite, Kerry Craig, global market strategist at J.P. Morgan Asset Management, said.

But he said support from central banks and governments should underpin markets, even amid uncertainty about the U.S. election and development of coronavirus vaccines. On Tuesday, AstraZeneca PLC paused trials of a Covid-19 vaccine after the unexplained illness of a study participant.

Daniel Gerard, senior multi asset strategist at State Street Global Markets, said aside from easy monetary policy and the recent rally in technology stocks, there were few factors driving markets. That made them fragile, he said. "When people get anxious, it ripples through the system quite quickly."

The most actively traded futures contract for Brent crude, the global oil benchmark, fell 0.6% to $39.56, while the equivalent for gold edged down 0.4% to $1,935 a troy ounce.

The yield on the benchmark 10-year U.S. Treasury note fell to 0.671%, from 0.682%. Bond yields fall as prices rise.

Anna Isaac

contributed to this article.

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