Shares in China fell 1.06% and Australian stocks shed 0.22% after the country's jobless rate jumped to the highest since the late 1990s. Shares in Hong Kong, and Seoul also fell.
Oil futures fell after OPEC and its allies agreed to scale back output cuts, renewing concerns over excess supply.
Risk appetite took a hit due to worries about a wide-ranging dispute between the United States and China over the control of advanced technologies and the protection of civil liberties in Hong Kong.
A second wave of coronavirus infections is also triggering a return to restrictions on business activity that threaten economic growth.
"The upside in financial markets is limited by the visible increase in coronavirus infections and tension between the world's two economic giants," said Masayuki Kichikawa, chief macro strategist at Sumitomo Mitsui Asset Management Co.
"However, the downside is limited due to very low interest rates and a brighter outlook for China's economy."
China's economy expanded by a better-than-expected 3.2% in the second quarter from a year earlier, returning to growth after a record contraction as lockdown measures ended and policymakers stepped up stimulus.
But its recovery is still uneven. Separate data showed China's industrial output beat expectations in June, but retail sales unexpectedly fell again, suggesting consumer demand remains weak.
U.S. Secretary of State Mike Pompeo on Wednesday said the United States would impose visa restrictions on Chinese firms like Huawei Technologies Co Ltd that he accused of facilitating human-rights violations. President Donald Trump's administration is also expected to take action in coming weeks to address perceived security risks posed by TikTok and WeChat, two popular Chinese mobile apps, a White House official said on Wednesday.
The moves would be the latest salvo in a dispute between Washington and Beijing that has unsettled investors.
Investors are also worried about jumps in coronavirus cases in the United States, Australia, and Japan.
But on Wall Street the S&P 500 gained 0.91% on Wednesday, boosted by hopes for a vaccine and a strong quarterly report from Goldman Sachs, but those gains failed to lift Asian stocks.
U.S. crude CLc1 fell 0.73% to $40.90 a barrel. Brent crude LCOc1 fell 0.5% to $43.57 per barrel following plans from OPEC and its allies to ease supply curbs.
In the currency market the Australian dollar, the New Zealand dollar, and the Chinese yuan all fell against the U.S. dollar amid rising risk aversion.
(Editing by Kim Coghill) ((firstname.lastname@example.org; +81 (0)3 4563 2799; twitter.com/stanleywhite1 ;))