Investors were also rattled by dimming hopes for more financial support for the US economy.
However, European markets opened slightly higher on Tuesday and London's 100 share index was up 0.4% at 5826.24 points.
Earlier, Australia's All Ordinaries ended down 0.7% at 5,973.50, Hong Kong's Hang Seng lost 1% to 23,720.06, the Shanghai Composite fell 1.3% to 3,274.30 while South Korea's Kospi dropped by 2.38%, to end at 2,332.59.
Stock markets in Asia suffered on Tuesday from the fallout from UK and US investors worried about a rise in coronavirus cases. Australia, Hong Kong, China and South Korea stock markets were all down.