The Chinese Shanghai Composite rose 0.48 percent, or 10.40 points, to 2163.71. Hong Kong's Hang Seng gained 0.15 percent, or 31.51 points, to 22542.91. Among major gainers were HSBC Holdings Plc (0.85 percent) and Swire Pacific Ltd (0.65 percent).
South Korea’s Kospi Composite Index rose 0.13 percent, or 2.49 points, to 1982.91. Shares of Samsung Electronics Co Ltd gained 1.32 percent and shares of LG Electronics Inc were down 0.95 percent. Stock markets in Japan are closed Monday for holiday.
India's BSE Sensex gained 0.15 percent or, 29.38 points, to 19271.38. Among the major gainers were Lanco Infratech Ltd (6.54 percent), Madras Cement (4.60 percent) and United Breweries Ltd (2.74 percent).
Investors are currently focusing on the US fiscal cliff. There is the worry that even if the U.S. President Barack Obama and the House Speaker John Boehner are able to reach an agreement, there is no guarantee that it will be able to attain the required number of votes in the House and the Senate.
“The negotiations to avert the fiscal cliff are, as we always expected, going down to the wire. This is supposed to be political theatre. The failure of Boehner's "Plan B" illustrates that any deal has to be a bipartisan one that the moderates on both sides can support, offsetting the opposition of the Tea Party sympathizing House Republicans and probably a few Democrats too. We still think such a deal is achievable by early January,” Capital Economics said in a note.
Investors are also expected to focus on the developments in the euro zone in the coming days with the European governments likely to press ahead with economic and fiscal reforms. There is the worry that reform process in Italy can be affected following the resignation of Mario Monti as Prime Minister Dec. 21.
Market players sense that in the weeks ahead the euro zone debt crisis could escalate if Germany is not willing to make a larger financial commitment needed to ensure the region’s economic and financial stability.