Adding to the gloomy sentiment, Cyprus became the fifth eurozone country out of the 17 countries in the bloc to seek a bailout.
Tokyo fell 0.81 percent, or 70.63 points, to 8,663.99, Seoul was 0.41 percent off, shedding 7.57 points to 1,817.81 and Sydney closed 0.36 percent, or 14.5 points, lower at 4,013.3.
Shanghai was flat, closing 2.04 points down at 2,222.07 but Hong Kong rebounded from three days of losses to end 0.45 percent, or 84.39 points, higher at 18,981.84.
Eyes are on the two-day meeting of EU leaders on Thursday and Friday as they try to overcome their differences to save the troubled euro.
But despite so much at stake – with Italy and Spain now in focus – investors say they do not expect any concrete plan to evolve owing to the divisions between the pro-growth and pro-austerity camps.
“Expectations are very low for the upcoming European summit,” said Tim Waterer, senior trader at CMC Markets in Sydney.
“There is a feeling that nothing concrete is going to come out of it and that we will be none the wiser about the solution to long-term problems,” he told Dow Jones Newswires.
On Tuesday morning French Finance Minister Pierre Moscovici said he would be holding talks with his counterparts from Germany, Spain and Italy in the run-up to the summit.
In a fresh blow, ratings agency Moody’s hit 28 Spanish banks with new credit downgrades Monday.
As Madrid formally requested a rescue loan of up to 100 billion euros ($125 billion) for the banking sector from its eurozone partners, Moody’s said the banks faced rising losses from commercial real estate loans.
The agency said Madrid’s own lowered credit grade also contributed to the rating cuts.
Moody’s last week cut the ratings of 15 of the biggest names in banking including Goldman Sachs, Barclays, Citigroup, HSBC and Deutsche Bank, citing their exposure to each other and the financial crisis.
On Monday Cyprus, which had a large exposure to Greek government debt, requested financial help from its eurozone partners, following Ireland, Greece, Portugal and Spain.
While it did not specify the amount, local media speculated it would be in the region of five billion euros.
On Wall Street the Dow fell 1.09 percent, the S&P 500 slid 1.60 percent and the tech-rich Nasdaq lost 1.95 percent.
In early European forex trade the euro fell to $1.2489 and 99.02 yen, compared with $1.2502 and 99.58 yen in New York late Monday.
The dollar bought 79.30 yen, compared with 79.67 yen.
Oil prices slipped. New York’s main contract, light sweet crude for delivery in August, slid 24 cents to $78.97 in the afternoon and Brent North Sea crude for August delivery dipped 21 cents to $90.80.
Gold was at $1,584.76 an ounce at 1050 GMT, compared with $1,569.01 late Monday.
In other markets:
— Singapore fell 0.34 percent, or 9.63 points, to 2,805.63.
Singapore Airlines lost 0.88 percent to Sg$10.18 and DBS Group Holdings eased 0.88 percent to Sg$13.53.
— Taipei fell 0.40 percent, or 28.45 points, to 7,137.93.
Chunghwa Telecom rose 0.88 percent to Tw$92.0 while TSMC was 1.13 percent lower at Tw$78.7.
— Manila closed 0.52 percent higher, adding 26.64 points to 5,193.84.
Philippine Long Distance Telephone rose 1.91 percent to 2,674 pesos while Ayala Corp. added 0.43 percent to 470 pesos.
— Wellington ended down 0.58 percent, or 19.80 points, at 3,381.32.
Telecom fell 1.42 percent to NZ$2.435, Fletcher Building was off 1.67 percent at NZ$5.88 and Contact Energy eased 0.21 percent to NZ$4.71.
— Jakarta rose 0.62 percent, or 23.81 points, to 3,881.40.
Nickel and gold miner Antam rose 3.8 percent to 1,380 rupiah, coal miner Adaro gained 4.5 percent to 1,390 rupiah and cement manufacturer Indocement rose 1.50 percent to 16,950 rupiah.
— Kuala Lumpur eased 0.56 percent, or 9.02 points, to 1,594.10.
YTL Corp. lost 2.9 percent to end at 2.00 ringgit, while Axiata Group slid 1.1 percent to 5.44 ringgit. AirAsia gained 0.3 percent to 3.61 ringgit.
— Bangkok ended 0.32 percent higher, adding 3.66 points to 1,151.09.
Banpu was unchanged at 438 baht, while PTT gained 0.32 percent to 311 baht.
— Mumbai edged up 0.14 percent, or 24.42 points, to 16,906.58.
India’s private Tata Power rose 1.7 percent to 95.5 rupees and state-run explorer Oil and Natural Gas Corp (ONGC) rose 1.52 percent to 277.1.