Asian shares climbed on Tuesday following a rebound in the final hour of New York trading as markets were seen to be pricing in an expected hefty Federal Reserve interest rate hike this week to tackle inflation.

"Many investors have already fully priced in a rise of 75 basis points at the Fed's meeting this week," said Zhang Zihua, chief investment officer at Beijing Yunyi Asset Management.

"The market will now pay close attention to the tone of speech coming out of the meeting. As long as the Fed officials don't deliver strong hawkish remarks, stock markets could [further] rebound."

China's blue-chip CSI300 index was 0.2 percent higher while Hong Kong's Hang Seng index rose 1.2 percent.

Sentiment in Hong Kong was also boosted after the government flagged easing of quarantine policy for all arrivals was coming soon.

MSCI's broadest index of Asia-Pacific shares outside Japan was up 1.2 percent while Australian shares climbed 1.2 percent.

In Japan, where trade resumed after a national holiday, the Nikkei advanced 0.48 percent with technology stocks largely driving the climb.

On Monday, the S&P 500 and the Nasdaq Composite rebounded after logging their worst weekly percentage drop since June. The S&P 500 gained 0.69 percent, the Nasdaq added 0.76 percent while the Dow Jones Industrial Average rose 0.64 percent.

(Source: Reuters with edits)