Japan's benchmark Nikkei 225 rose 1.5% to a fresh record, after closing at an all-time high Monday . The Topix also added 0.73% to hit a record high.
Broader Asia-Pacific markets also opened higher, tracking Wall Street gains, led by a rally in Apple shares.
Investors await Japan's parliamentary vote, which is likely to see Sanae Takaichi become the country's next prime minister, after the right-wing opposition Japan Innovation Party said Monday it was ready to back her premiership.
South Korea's Kospi index jumped over 2%, led by gains in heavyweight auto stocks, to hit a fresh high. Shares of Hyundai Motor climbed 6.45%, while Kia Corp added 4.28%.
Australia's ASX/S&P 200 rose 0.50%. Shares of the country's rare earth companies rose after Prime Minister Anth