Japan's Nikkei 225 stock average rose 0.4 percent to 9,556.27, following a nearly 4 percent plunge Monday. Exporters benefited as the yen eased against the euro.
Hong Kong's Hang Seng index inched up 0.1 percent to 19,397.39, and Australia's ASX/S&P 200 climbed 1.2 percent to 4,377.80.
Benchmarks in mainland China, South Korea and Singapore also climbed. In negative territory were shares in Taiwan and New Zealand.
Reaction to Bernanke Comments
In remarks Monday night, Bernanke said he is hopeful the economy will gain traction and not fall back into a "double dip" recession.
"My best guess is we will have a continued recovery, but it won't feel terrific," Bernanke said.
Concerns have grown that the recovery could be derailed if Europe's debt crisis turns into a broader financial contagion, crimping lending in the United States and around the globe. The situation has spooked investors, sending Wall Street into fits of panic.
Bernanke said the Fed is carefully monitoring the European crisis, and he believes European leaders are taking the right steps.
On Wall Street Monday, the Dow Jones industrial average lost 1.2 percent to 9,816.49, its lowest finish since November. The S&P 500 index fell 1.4 percent to 1,050.47, and the Nasdaq composite index fell 2 percent to 2,173.90.
In currencies, the dollar rose to 91.84 yen from 91.40 yen late Monday. The euro rose to $1.1963 from $1.1916.
Benchmark crude for July delivery was up 13 cents at $71.57 a barrel in electronic trading on the New York Mercantile Exchange.