Asian markets opened higher on Tuesday following Monday's late rally on Wall Street.
Benchmark oil rose to near $89 a barrel while the dollar slipped against the yen and the euro.
Japan's benchmark Nikkei 225 index was up 0.3 percent at 8,561.97. Australia's S&P/ASX200 index was up 0.6 percent to 4,063.20. New Zealand's benchmark NZX 50 was up 0.4 percent to 3,276.71.
Mainland Chinese stocks opened lower, with the benchmark Shanghai Composite Index down 1.7 percent to 2,454.17. The smaller Shenzhen Component Index was 2.2 percent lower at 1,070.21.
Markets in Hong Kong and Korea were closed for public holidays.
The Dow Jones Industrial index ended Monday up nearly 69 points, or 0.6 percent, at 11,061 after a late afternoon rally pushed the stock market higher.
The Dow Jones industrial average rose 0.6 percent to close at 11,061.12, with all of the gains coming in the last 10 minutes of trading.
Traders said a combination of technical factors and reports that China was buying Italian government bonds triggered the late spurt of buying.
The S&P 500 index rose 0.7 percent to close at 1,162.27. The tech-heavy Nasdaq composite index rose 1.1 percent to 2,495.09.
Markets in Europe and Asia plunged Monday as investors worried that Greece could be edging closer to default.
Greece is being kept solvent by a $150 billion international rescue loan package, while an agreement in July to double the bailout size has yet to be implemented. The cash lifeline, without which the country would go broke in a few weeks, is conditional on Athens meeting its ambitious savings targets.
The euro rose slightly to $1.3670 from $1.3666 in New York late Monday. Earlier that day, the European common currency hit $1.3495, a seven-month low. The euro started the month around $1.43. The euro also hit a 10-year low against the Japanese yen.
The dollar dipped to 77.10 yen from 77.25 yen.
Benchmark crude for October deliver rose 78 cents to $88.94 a barrel in electronic trading on the New York Mercantile Exchange.
In London, Brent crude for October delivery was up 77 cents at $110.96 on the ICE Futures exchange.
