Equities lost out and the euro slumped as traders sought out safe haven assets to take shelter from the gloom, with gold hitting another record high.
Tokyo fell 2.21 percent, or 193.89 points, to 8,950.57, its lowest level since April 2009, while Seoul ended 1.07 percent, or 19.12 points, lower at 1,766.71 and Sydney shed 1.60 percent, or 66.4 points, to 4,075.5.
In the afternoon Hong Kong gave up 1.47 percent and Shanghai was 0.52 percent off.
The falls extended selling from Monday after a dismal batch of US jobs data raised concerns of a double-dip recession in the world's biggest economy.
They also followed massive losses in Europe, where financials were heavily hit after International Monetary Fund chief Christine Lagarde warned banks needed extra capital to withstand any contagion from the eurozone debt crisis.
The head of the European Central Bank Jean-Claude Trichet also warned Monday of an immediate and imperative need for enactment of a second debt rescue for Greece, and tightened discipline in the management of eurozone economies.
London's FTSE 100 dropped 3.58 percent, in Paris, the CAC 40 fell 4.73 percent and Frankfurt's DAX plunged 5.28 percent to a two-year low.
US markets were closed on Monday for the Labor Day bank holiday.
Adding to the European woes was news the European Union and International Monetary Fund left a critical audit of Greek finances unfinished saying more budget work was needed, while Athens admitted its deficit target was in trouble.
Also negative for the euro was news that German Chancellor Angela Merkel's Christian Democrats (CDU) suffered an election defeat in her home state Sunday, with the news unsettling the market, dealers said.
Selling of bank stocks was exacerbated by a US decision to take legal action against 17 leading international lenders over securitised mortgage trading at the heart of the 2008 financial crisis.
ECB data showed that eurozone banks have deposited record amounts of overnight funds with it, a signal of reluctance by banks to lend to each other.
The ongoing troubles in the eurozone weighed on the region's currency.
The euro fell to a one-month low of $1.4062, compared with $1.4109 late in London Monday.
It was also at 107.94 yen from 108.57 yen.
The dollar bought 76.75 yen compared with 76.86 yen in London.
The price of gold hit a record high 1,920.90 an ounce at 0600 GMT.
"The Greek debt problem is of utmost concern on most investors' minds," said Hideyuki Ishiguro, a strategist at a Japanese securities firm, noting the upcoming Greek sovereign debt rollover deadline.
"It's too scary to buy stocks before we find out how this will pan out," he told Dow Jones Newswires.
And Tim Condon, economist at ING, said: "The selloff in European risk assets is becoming disorderly. US Treasuries may be a preferred safe-haven asset but Asian local currency government bonds also are candidates."
On oil markets New York's main contract, light sweet crude for delivery in October, dived $2.82 to $83.63 per barrel.
Brent North Sea crude edged up 29 cents to $110.37.
In other markets
Taipei fell 2.44 percent, or 184.38 points, to 7,367.19.
Leading design house MediaTek fell 3.86 percent to Tw$274.0 while Formosa Plastics was 3.52 percent lower at Tw$85.0
Manila closed 1.81 percent, or 79.48 points, lower at 4,303.08.
Lepanto Mining fell 2.6 percent to 1.50 pesos, San Miguel tumbled 4.0 percent to 120 pesos and Metropolitan Bank slid 3.5 percent to 70.45 pesos.
Wellington fell 0.69 percent, or 22.57 points, to 3,270.56.
Telecom rose 1.7 percent at NZ$2.44, Fletcher Building closed unchanged at NZ$7.58 and Auckland Airport fell 3.0 percent to NZ$2.26.