Chinese Shanghai Composite fell 0.42 percent or 8.68 points to 2069.82. Hong Kong's Hang Seng was down 0.09 percent or 18.46 points to 20639.65. Among the major losers were China Life Insurance Co Ltd (1.09 percent) and CNOOC Ltd (2.59 percent).
South Korea's KOSPI Composite Index fell 0.07 percent or 1.34 points to 2001.01. Shares of Samsung Electronics Co Ltd rose 0.23 percent and those of LG Electronics Inc advanced 0.13 percent.
Japan's Nikkei Stock Average was up 0.15 percent or 14.15 points to 9173.54. Among the major gainers were Sumco Corp (4.18 percent), Sony Corp (3.87 percent) and Advantest Corp (3.78 percent).
India's BSE Sensex dropped 0.10 percent or 19.32 points to 18522.99. Among the major losers were Jaiprakash Associates (1.16 percent), ICICI Bank (1 percent) and Sesa Goa (0.91 percent).
The relationship between China and Japan took a bad turn after Tokyo last week said that it would buy the East China Sea islands claimed by both countries. The purchase of the islands for 2.05 billion yen ($26 million) was approved by Japan's cabinet Sept 11.
Investors worry that the dispute over these islands, called Senkaku in Japan and Diaoyu in China, could result in a trade fight between the two Asian economic powerhouses. Market players are concerned that the dispute between the world's second and third largest economies could further weaken the global economic growth already affected by the euro zone crisis.
Protesters in China have called for boycott of goods from Japan. Japanese companies such as Toyota Motor Corp, Honda Motor Co and Nissan Motor Co. have stopped production at certain plants in China. Japan has asked Beijing to make sure that Japanese businesses are provided the required safety in China.
Investors continue to worry about the euro zone situation. Market participants feel that the rising tensions within the Troika, consisting of the European Commission, the European Central Bank and the International Monetary Fund, could prompt the withdrawal of Greece's bailout.