Equities in Asia gained in Tuesday trade, markets benefiting from Wall Street's strong lead and subsiding risk aversion.

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Japan's Nikkei 225 rose 1.34 percent as the greenback strengthened against the yen, after the index finished lower by close to 1 percent in the previous session.

Down Under, the S&P/ASX 200 tacked on 0.62 percent, with the index driven by gains in the health care and Australian real estate investment trusts sub-indexes. The heavily-weighted financials sub-index gained 0.82 percent.

Greater China markets also trended higher, with Hong Kong's Hang Seng Index up 0.45 percent and mainland markets holding onto gains made in the previous session. The Shanghai Composite climbed 0.30 percent while the Shenzhen Composite edged higher by 0.125 percent.

The gains in Asia came after major indexes stateside closed the Monday session significantly higher as investors looked past geopolitical tensions that had clouded markets for most of last week. The Dow Jones industrial average gained 0.62 percent, or 135.39 points, to end at 21,993.71. The CBOE Volatility Index (VIX), widely considered the best gauge of fear in the market, traded near 12.3, down about 20 percent.

The dollar was mostly stable against a basket of currencies following overnight gains, with the dollar index at 93.471 at 9:44 a.m. HK/SIN. The greenback also firmed against the yen, with the US currency last fetching 110.17 yen. That was above levels around 109.15 seen last Friday.

"Traders cited the easing of tensions with North Korea as the war of words appears to have abated, but the move appeared to be a classic short covering rally as the dollar rebounded after several days of heavy selling," said BK Asset Management Managing Director of FX Strategy Boris Schlossberg in a Monday evening note.

Tensions appeared to de-escalate further, as North Korean leader Kim Jong Un told state media Tuesday that he would observe actions taken by the US before making further decisions, Reuters reported. North Korea had said last week it was considering plans to strike Guam.

In corporate news, Melco International Development proposed a spin-off for its Macau resort Studio City, with plans to list the unit in the US, the company said in a filing to the Hong Kong Exchange Monday evening. Melco's stock was up 3.72 percent on the news, outperforming other Hong Kong-listed gaming plays: Wynn Macau was up 2.10 percent and Galaxy Entertainment rose 1.40 percent.

Also of note, the Commonwealth Bank of Australia may claw back bonuses from executives if required, the Australian Financial Review reported Monday, citing the bank's chairman Catherine Livingstone. CBA Chief Executive Ian Narev's bonus was scrapped last week as the lender deals with a money-laundering scandal.

CBA stock was up 0.44 percent, in line with broader gains in Australian financials: ANZ rose 1.39 percent after reporting a 5.3 percent rise in third-quarter cash profit while National Australia Bank advanced 1.14 percent.

Meanwhile, the Australian dollar spiked inched up 0.3 percent against the dollar after the Reserve Bank of Australia warned of the currency's strength and household debt levels in minutes of the central bank's latest policy meeting.

Other market movers included Toshiba. The stock jumped 4.88 percent as Citi analysts upgraded the Japanese firm to "buy/high risk" from "neutral" in an Aug. 14 note. Toshiba shares were still a "risky investment," but the possibility of delisting has decreased, the note said.

Also in Japan, Fujifilm shares jumped 7.58 percent after the company reported record profit in the quarter ending in June on Monday, according to Reuters.

On the energy front, oil prices climbed slightly after falling more than 2.5 percent overnight. Brent crude edged up 0.18 percent to trade at USD 50.82 a barrel and US West Texas Intermediate crude was up 0.15 percent at USD 47.66. Oil fell on Monday as the dollar recovered and soft China demand data revived investor worries about oversupply in oil markets, according to Reuters.