The benchmark Nikkei 225 index added 1.20 percent, or 317.84 points, to 26,844.66 in early trade, while the broader Topix index climbed 0.91 percent, or 17.23 points, to 1,904.16.

The dollar stood at 115.05 yen, compared with 114.93 yen seen Monday in New York.

The Dow fell 0.5 percent, but the Nasdaq added 0.4 percent.

The Tokyo market lifted as investors' aversion to risk softened after US shares avoided sharp drops despite earlier concerns that broad financial sanctions against Russia and its banking institutions could dent the global economy.

"US shares were mixed [...] A sense of relief should cover Tokyo shares," Okasan Online Securities said in a note.

"Once early buying subsides, we expect investors to take wait-and-see positions ahead of the release of ISM data [for US manufacturing activities] later today and Fed Chair [Jerome] Powell's Congressional appearance tomorrow," it added.

Overnight, Raphael Bostic, president of Federal Reserve Bank of Atlanta, said he favored raising interest rates by 25 basis points in March while adding that a 50-basis-point hike was also possible depending on the level of inflation.

"There are many major economic events expected in the US, and the market's focus may shift to US monetary policy," Okasan said.

All eyes also remain on Ukraine, with leading democracies imposing broad sanctions targeting assets of Russian leaders and Russian financial institutions. 

"The sense of uncertainty for the global economic outlook may increase as the US, Europe and Japan impose sanctions, but hopes for cease-fire negotiations are providing support for the market," Okasan said.

"The market will remain sensitive to news headlines," it said.

Among major shares, Toyota began the day in red but emerged above water and was trending up 0.02 percent to 2,139 yen by mid-morning, as the world's biggest automaker shuts down its domestic factories after a reported cyberattack on a parts supplier.

Troubled engineering conglomerate Toshiba was also up 3.87 percent to 4,754 yen after local media reported on plans for chief executive and chairman Satoshi Tsunakawa to step down.

The firm's management is facing loud opposition from some investors about its reform initiatives and plans to spin off a segment of its business, after allegations management attempted to weaken the influence of activist investors.

SoftBank Group rose 3.63 percent to 5,311 yen. Uniqlo-operator Fast Retailing advanced 2.57 percent to 63,420 yen. Sony edged up 0.25 percent to 11,840 yen.

Meanwhile, Hong Kong stocks opened with small gains Tuesday as the Hang Seng Index rose 0.41 percent or 94.10 points to 22,807.12.

The Shanghai Composite Index gained 0.63 percent or 21.70 points, to 3,484.01, while the Shenzhen Composite Index on China's second exchange edged up 0.27 percent or 6.14 points, to 2,324.24.