Japan's Nikkei 225 index plunged 4.8 percent to 8,662.30 in the morning session, while Hong Kong's Hang Seng index plummeted 18,981.55.
Elsewhere, Australia's benchmark S&P/ASX-200 index lost 4.9 percent to 3,790.50. Taiwan's TAIEX dropped 4.9 percent and New Zealand's benchmark NZX 50 index shed 3.7 percent.
Michael McCarthy, chief strategist at Sydney-based stockbroker CMC Markets, attributed the market turbulence to fears that the U.S. economy was slowing down.
"We're clearly in fear territory," McCarthy said. "The major driver here seems to be weakness in the U.S. economy. There are fears that it's starting to stall and if that's the case, the whole global growth scenario could fall over."
Shane Oliver, chief economist of Australian investment manager AMP Capital, said he was surprised that the Australian market had not stabilized Tuesday after steep falls on the previous two trading days.
"I would have thought we would have factored in a lot of the weakness, but obviously the fall on Wall Street was greater than Australian investors and Asian investors expected this time yesterday," Oliver told Australian Broadcasting Corp. television.
The losses come on the heels of a rout on Wall Street on Monday, the first trading day since ratings agency Standard & Poor's downgraded American debt.
The Dow Jones industrials fell 634.76 points, the sixth-worst point decline for the Dow in the last 112 years and the worst drop since December 2008. Every stock in the Standard & Poor's 500 index declined.
Worries about the U.S. economic recovery have been building since the government said that economic growth was far weaker in the first half of 2011 than economists expected. Intensifying concerns were reports showing that the manufacturing and services industries barely grew in July, although job growth was better than economists expected last month.
Investors are also worried that Italy and Spain could become the next European countries to have trouble repaying their debts. Greece, Ireland and Portugal have already received bailout loans because of Europe's 21-month-old debt crisis.
The fears have pushed investors to shun Spanish and Italian bonds, which have led to higher yields and in even higher borrowing costs for the two countries.
The European Central Bank stepped in Monday and bought billions of euros worth of their bonds. The move helped to lower yields on Spanish and Italian bonds, at least temporarily.