The Tokyo stock exchange's Nikkei 225 was up 0.6 percent when investors took a break for lunch, while the broader Topix index indicated a plus of 0.8 percent.
The Hong Kong Hang Seng was traded just above zero, while Shanghai and Shenzhen's composite index were up 0.4 and 0.2 percent, respectively.
South Korea's Kospi index was up 1.1 percent.
Trading in Asia follows Monday's gains on Wall Street, where the broad S&P 500 index rose 1.5 percent and the technology-heavy Nasdaq composite index climbed 2 percent, while the Dow Jones industrial index landed at a plus of 1.3 percent.
