The Hang Seng Index opened 0.3% lower and China's benchmark CSI300 Index slid 0.7% at the start.
In Beijing, policymakers kept the benchmark lending rate for corporate and household loans unchanged at its July fixing on Tuesday, despite growing expectations for a cut after a surprise lowering of bank reserve requirements.
"The markets are clearly on risk-off mode," said Edison Pun, senior market analyst at Saxo Markets, adding that Wall Street's uptrend is weakening.
Stocks on Wall Street fell as much as 2% on Monday, with the Dow posting its worst day in nine months as COVID-19 deaths increased in the United States.
Riskier assets globally have come under pressure recently as many countries struggle to contain the outbreak of the fast-spreading Delta virus variant, raising fears that further lockdowns and other restrictions could upend the worldwide economic recovery.
"Despite the vaccine rollout, markets do not appear to be learning to live with COVID-19," ANZ analysts wrote in a note to clients.
"Sentiment appears to have shifted, at least for the moment, to a persuasion that growth and earnings expectations may be overdone," they said, noting that risk-averse investors were bailing out of commodities.
Oil prices plunged more than 6%, driven down both by worries about future demand and by an OPEC+ agreement to increase supply.
U.S. yields turned higher on Tuesday following Monday's searing rally. The 10-year yield rose to 1.2087% from a close of 1.181%, a level last seen in February, and the 2-year yield edged up to 0.2196% from 0.21% Tuesday.
However, while the U.S. yield curve steepened slightly, the spread between the U.S. 10-year and 2-year yield remained near February lows, signalling investor doubts about the growth outlook.
Japan's core consumer prices rose 0.2% in June from a year earlier to mark the fastest annual pace in over a year, driven largely by higher energy costs, a sign the impact of global commodity inflation was gradually broadening.
U.S. crude managed to steady and paresome of Monday's losses, up 0.74% at $66.91 a barrel, while Brent also recovered to gain 0.45% at $68.93 a barrel. However, both were still down sharply from the end of last week.
Spot gold was steady at $1,813.15 per ounce, after falling to a one-week low of $1,794.06 in the previous session.
(Reporting by Kane Wu in Hong Kong; additional reporting by Andrew Galbraith in Shanghai Editing by Shri Navaratnam) ((firstname.lastname@example.org; +85228436590; Reuters Messaging: email@example.com))