The Japanese benchmark Nikkei fell 0.81 percent or 70.63 points to 8,663.96, South Korean KOSPI declined 0.41 percent or 7.57 points to 1,817.81 and Indian benchmark BSE Sensex declined 0.33 percent, while Chinese Shanghai Composite ended flat and Hong Kong's Hang Seng advanced 0.45 percent.
Investor sentiment continues to weigh down due to concerns that European Union leaders' two-day meeting in Brussels won't come up with any substantial measures to tackle the debt crisis.
Expectations are very low for the upcoming European summit. 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, Tim Waterer, senior trader at CMC Markets in Sydney, told the Wall Street Journal.
Raising further concerns are Spain and Cyprus, as both countries have made a formal request for funds from the EU. Cyprus became the fifth euro zone nation to seek rescue in a crisis that's now threatening to enter its third year. Spain has also formally requested EU aid to help finance its ailing banking system, but the exact amount will not be known until a memorandum of understanding is signed between the two parties July 9.
Meanwhile, Moody's Investors Service downgraded the long-term debt and deposit ratings of 28 Spanish banks Monday, including Banco Santander and Banco Bilbao Vizcaya Argentaria, citing the reduced creditworthiness of Spanish government bonds and the banks' links to sovereign debt along with the its sour real estate loans.
In Japan, exporter and financial companies' shares declined on a stronger yen and bad news from Europe. Sony Corp. fell 2.91 percent and Mizuho Financial Group Inc. declined 2.36 percent while Canon slipped 1.42 percent.
Toyota Motor Corp. fell 1.14 percent and Honda Motor declined 1.54 percent after Chinese officials declared that the government had no imminent plans to introduce more stimulus policies to help revive vehicle demand in the world's biggest auto market, Bloomberg reported.
Energy companies' shares were among the top losers in China. China Coal Energy Co fell 0.63 percent and Yanzhou Coal Mining plunged 5.36 percent while PetroChina Co fell 0.44 percent.
Seoul shares ended lower for the fourth day Tuesday as European crisis continued to weigh on sentiment. Samsung Electronics advanced 0.62 percent after slumping more than 9 percent in the last three sessions.