One of the biggest gains was in Japan after a few days off over the weekend. Japan's Nikkei 225 surged 5.7 percent while the broader Topix climbed 3.4 percent.
The Hong Kong-based Hang Seng also rose 1.5 percent.
In China, the increases were somewhat more modest, with Shanghai and Shenzhen up 0.2 percent and 0.3 percent, respectively.
South Korea's Kospi fell 0.4 percent.
