Nikkei adds 0.6%
Japan's Nikkei 225 clawed back some of Monday's 2.9 percent slump.
Gainers were led by airlines, which got a boost from the tumble in jet fuel prices. Japan Airlines and ANA Holdings climbed 1.7 and 2.9 percent, respectively. A recovery in most export-oriented counters also supported the bourse; carmakers such as Toyota Motor, Nissan and Honda bounced up between 0.6 and 1.2 percent.
However, shares of Sony fell 8.3 percent after the company said it plans to raise up to $3.6 billion by issuing new shares and convertible bonds to invest in its fast-growing image sensors business.
Meanwhile, Japan Post will be filing applications with the Tokyo Stock Exchange for the listings of the parent company and its units Japan Post Bank and Japan Post Insurance on Tuesday.
Kospi gains 0.7%
South Korea's Kospi index edged up, a day after finishing at a one-week low.
Beneficiaries of cheaper oil were among the day's top performers; Korean Air Lines and Asiana Airlines jumped 6.9 and 4.6 percent, respectively, while Kepco tacked on 1.2 percent.
Samsung Techwin inched up 0.2 percent after shareholders on Monday approved a proposed deal to be sold to Hanwha Group. Shares of the latter recouped losses to rise 2.2 percent late Tuesday.
ASX rises 0.7%
Australian shares ended up in choppy trade, which saw the benchmark S&P ASX 200 index hit a five-month low at the start of trade. Apart from Greece, investors trying to close their books for the June 30 end of the financial year fueled volatility in the market on Tuesday.
The bourse gained upward support after banking heavyweights turned positive in the final hour of trade. Commonwealth Bank of Australia rebounded 0.5 percent, while Westpac and National Australia Bank closed up 0.4 percent each.
Within the resources sector, market bellwether BHP Billiton clawed back losses to settle 0.4 percent higher.
Meanwhile, New Zealand-listed Briscoe Group announced it has acquired 19.9 percent of clothing retailer Kathmandu early Tuesday, sending the latter's Sydney-listed stock up 25.6 percent. In Auckland, shares of Briscoe Group rallied 1.8 percent, while Kathmandu surged 25.9 percent.