The Tokyo stock exchange's Nikkei 225 index and the broader Topix index were up 0.7 percent shortly after lunch local time.
Hong Kong's Hang Seng index was simultaneously down 1.2 percent, while Shanghai's composite index pointed to a minus 0.2 percent.
South Korea's Kospi index, on the other hand, pointed up 0.5 percent.
Fears that the clashes between Israel and Iran will spread have contributed to pushing up the oil price. The price of so-called Brent oil has risen to over 76 dollars per barrel.
Fears about how the situation in the Middle East can affect the global economy are also contributing to lowering the stock market mood, the three leading indexes on Wall Street fell on Tuesday evening. The broad S&P 500 index fell 0.8 percent, the Dow Jones industrial index fell 0.7 percent, while Nasdaq's technology-heavy composite index closed at a minus 0.9 percent.
On Wednesday, the US central bank, the Federal Reserve, will announce its interest rate decision.
