The momentum in Japanese markets was largely driven by the country's technology and financial sectors.
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Japan's main indexes rose more than 2% on Tuesday as markets resumed trading after a holiday.
The benchmark Nikkei 225 index rose 2.72%, breaking above the 36,000 level for the first time since Aug. 2. The broader Topix index also rose 2.25%.
The momentum was largely driven by the country's technology and financial sectors, with Rakuten Group and Trend Micro They jumped by more than 8% and 6% respectively.
Reuters news agency, citing government sources, reported that the country's parliament plans to hold a special session next week to discuss the Bank of Japan's decision to raise interest rates last month.
Japan's producer price index rose 3% in July from a year earlier, rising at a faster pace than the 2.9% increase in June.
South Korea's Kospi fell 0.2%, while the smaller-cap Kosdaq lost 1.57%.
Wages in Australia rose 0.8% in the quarter to June, the slowest pace since the same quarter last year, compared with estimates for a 0.9% rise. Wages were up 4.1% on an annual basis.
Australia's S&P/ASX 200 rose 0.16%.
Hong Kong Hang Seng Index China's stock index opened the trading day up 0.4%, while the CSI 300 index in mainland China opened up 0.06%.
In Southeast Asia, Singapore said its economy grew 2.9% in the second quarter from a year earlier, in line with its advance GDP estimate released in July. The Ministry of Trade and Industry pointed to strength in wholesale trade, finance and insurance, as well as the information and communications sectors. The city-state also said it expects GDP growth in 2024 to be between 2% and 3%, up from its previous forecast of 1% to 3%.
US markets faced a volatile session overnight as investors prepared for key inflation data.
The S&P 500 ended the day flat at 5,344.39, while the technology-dominated Nasdaq Composite rose 0.21% to close at 16,780.61, led by stocks Nvidia On the other hand, the Dow Jones Industrial Average fell by 140 points, or 0.36%, to close at 39,357.01 points.
Traders are awaiting the release of the July consumer price index on Wednesday, a leading indicator of the health of the US economy. Investors will be parsing the data for clues on whether the Federal Reserve will start cutting interest rates in September.
—CNBC's Brian Evans and Tanya Machel contributed to this report.
