Japan's Nikkei 225 index ended the morning session down 5.3% and Hong Kong's Hang Seng dropped 4.7%.
It comes after the Dow Jones Industrial Average suffered its worst drop in more than six years on Monday.
A strengthening global economy and healthy corporate earnings had spurred world markets to record highs.
But the sell-off began last week after a solid US jobs report fuelled expectations that the Federal Reserve will raise interest rates faster than expected.
