Chinese Shanghai Composite marginally rose 0.06 percent or 1.18 points to 2060.33 and Hong Kong's Hang Seng was down 0.17 percent or 33.35 points to 19525.86. Among major losers were Sino Land Co Ltd (1.23 percent) and China Overseas Land & Investment Ltd (0.99 percent).
South Korea's KOSPI Composite Index marginally dropped 0.03 percent or 0.54 points to 1912.17. Shares of Samsung Electronics Co Ltd rose 0.16 percent and those of LG Electronics Inc dropped 2.01 percent.
Japan's Nikkei Stock Average was down 0.09 percent or 7.65 points to 8776.24. Among major gainers were Japan Tobacco Inc (3.89 percent), Softbank Corp (2.84 percent) and Takashimaya Co Ltd (1.80 percent).
India's BSE Sensex fell 0.15 percent or 31.80 points to 17352.60. Among major losers were Bajaj Auto Ltd (0.87 percent), Tata Consultancy Services (0.30 percent) and Infosys (0.15 percent).
European Union President Herman Van Rompuy will meet German Chancellor Angela Merkel in Berlin Tuesday. They are expected to discuss the measures to be taken to overcome the current debt crisis and the steps necessary to stabilize the euro zone. The discussion is expected to include rules and commitments that the member states will have to follow to foster economic growth and financial stability.
French President Francois Hollande will meet Italian Prime Minister Mario Monti in Rome Tuesday. They are expected to address the sovereign debt crisis and measures to combat the situation. Investors will be waiting for the outcomes of the meeting. Expectations of announcement of stimulus measures by policymakers have helped bring down Italian 10-year yields below a critical level of 6 percent.
Meanwhile, rating agency Moody's downgraded the European Union's outlook to negative from stable. But it maintained the long-term and medium-term bond ratings at Aaa.
Market players will be focusing on the European Central Bank meeting in Frankfurt Thursday. Investors sense that the policymakers in the euro zone will need to urgently follow their words with action.