The Nikkei advanced 201 points to 10,513 as banking stocks rebounded after a recent decline.
Hang Seng moved up 218 points to 21,069 with China bank stocks leading rally on hopes that Beijing was unlikely to clamp down on lending ahead of national day celebrations in October.
The Sanghai Composite, however, shed 21 points to 2,925 on profit booking ahead of the country's August economic data.
The Straits Times and the Seoul Composite added 28 points and 37 points to 2,678 and 1,644, respectively.
The Taiwan Weighted gained 81 points to 7,332.
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(Updated 1140 hrs)
Asian markets have continued to trade in the green, led by oil stocks after OPEC decided to keep output steady.
The Hang Seng has surged 444 points (2%) to 21,295. The Nikkei has added 203 points (2%) to 10,515 on buying in banking shares.
The Straits Times and the Seoul Composite have gained 2% each at 2,705 and 1,642, respectively.
The Taiwan Weighted has advanced 87 points (1%) to 7,332.
The Shanghai Composite is flat at 2,949.
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(Updated at 0800 hrs)
The Asian markets have opened on a strong note and barring the Shanghai Composite.
The Hang Seng has advanced 306 points (1.5%) to 21,153. The Nikkei added 141 points (1%) to 10,452.
The Straits Times has moved 35 points (1%) to 2,685. The Seoul Composite and the Taiwan Weighted Index are up 1.5% each at 2,688 and 1,627, respectively.
While the Shanghai Composite is down 11 points at 2,935.
