The Nikkei 225 index was up 1.7 percent when traders took a lunch break, with the Topix index up 1.2 percent.
In Hong Kong, the Hang Seng index fell back by 1.5 percent, following larger increases on Monday.
Shanghai's composite index was up 0.1 percent, while Shenzhen's composite index fell back 0.2 percent.
Risk appetite is back since the world's two largest economies agreed to cut import tariffs on each other by 115 percentage points over a 90-day period.
All major indexes on Wall Street surged on Monday. The broad S&P 500 index closed at plus 3.3 percent, the Dow Jones industrial index lifted 2.8 percent and the technology-heavy Nasdaq composite index closed up 4.4 percent.
