Japanese share benchmark, the Nikkei 225, closed near flat, up 0.02 percent or 3.09 points at 19,253.61.
A bill to legalize casinos in Japan cleared an important parliamentary panel on Truesday, and is expected to be approved by the full chamber of the upper house on Wednesday. The casino legalization bill had already passed the lower house on Dec. 6.
The Bank of Japan's Tankan survey showed that an uptick in the sentiment of Japan's major manufacturers, with the headline index at plus 10 in the fourth-quarter, but expected to fall to plus 8 over the next three months.
Australia's ASX 200 finished up 0.71 percent or 39.55 points at 5,584.6, buoyed by gains across all sub-indexes except for materials, which was down 0.19 percent and energy, which was down 0.07 percent.
Shares of betting and lottery business Tatts rose 8.45 percent to A$4.49 each, after rising up 12 percent earlier. Macquarie Group and KKR offered to buy Tatts for A$7.3 billion ($5.5 billion) in a counterbid after Tabcorp agreed to buy Tatts in a deal valued at A$6.4 billion ($4.9 billion) in October. Tabcorp stock fell 0.86 percent to A$4.61.
The Shanghai composite closed 0.45 percent or 14.24 points at 3,140.8, as the Shenzhen composite lost 0.811 percent or 16 points at 1,959.86. Chinese markets have been under recent pressure due to new stock investment regulations on Chinese insurers and negative sentiment arising from Trump's comments on the "One China" policy.
In South Korea, the Kospi ended up 0.04 percent or 0.89 points at 2,036.87 after but wavering between gains and losses, while Hong Kong's Hang Seng added 0.28 percent by mid-afternoon..
Oil prices fell more than 1 percent in Asian trade, after American Petroleum Institute data showed surprise increases in U.S. crude inventories. The U.S. crude stumbled 1.34 percent to $52.27 a barrel as global benchmark Brent was off 1.22 percent to $55.04.