MSCI's broadest index of Asia-Pacific shares outside Japan .MIAPJ0000PUS was up 0.2 percent.
Investors remain wary ahead of Thursday's British vote, as well as Federal Reserve chief Janet Yellen's two-day testimony before Congress starting later on Tuesday, as she might offer clues on the timing of the next U.S. interest rate increase.
"With Yellen's congressional testimony and the UK referendum on our doorstep, markets all around are exercising caution," said Andrew Meredith, co-managing director at Tyton Capital Advisors.
Japan's Nikkei share average rose on Tuesday in choppy trade, as a weakening yen supported sentiment, but trading was thin as investors stayed cautious amid hopes Britain will stay in the European Union in this week's referendum.
The Nikkei rose 1.3 percent to 16,169.11 after traversing positive and negative territory.
China stocks surrendered initial gains and closed lower on Tuesday, a reflection of weak investor sentiment amid worries about the economy.
The CSI300 index of the largest listed companies in Shanghai and Shenzhen fell 0.2 percent, to 3,106.32, while the Shanghai Composite Index lost 0.4 percent, to 2,878.56 points.
Hong Kong stocks rose on Tuesday, as investor sentiment in global equity markets continued to improve on growing expectations that British voters will opt to remain in the European Union in this week's referendum.
The Hang Seng index rose 0.8 percent, to 20,668.44, while the China Enterprises Index also gained 0.8 percent, to 8,704.40 points.
Reference: Reuters
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