Hopes that central banks in China, the U.S. and Europe are gearing up for more stimulus measures to help their respective economies are keeping markets buoyant.
But Tom Kaan of Louis Capital Markets in Hong Kong said investors were holding back from big moves as the summer season winds down and eurozone leaders return from vacation to resume deliberating the region's debt crisis.
"I think if you look around globally, even on Wall Street, the volumes are pretty dismal," Kaan said.
Japan's Nikkei 225 rose 0.3 percent to 8,911.59, while Hong Kong's Hang Seng added 0.2 percent to 20,130.15. South Korea's Kospi rose 0.6 percent to 1,945.16, and Australia's S&P/ASX 200 gained 0.3 percent to 4,294.30.
Benchmarks in Singapore, Taiwan and New Zealand also rose, while mainland China's Shanghai Composite Index and Shenzhen Composite Index were both lower.
Traders were also waiting for the release of retail sales data from the U.S. for a clearer temperature reading of the health of the world's biggest economy. Other U.S. economic data this week includes July industrial production figures.
Meanwhile, Greece said Monday that the country's deep recession had eased slightly, although the economy still contracted 6.2 percent in the second quarter from the same period last year. In the first quarter, the contraction was 6.5 percent.
Stan Shamu of IG Markets in Melbourne, Australia, said in an email commentary that "the pace of Greece's economic meltdown was not quite as steep as the few economists who try to forecast the data expected."
Greece is being kept solvent by international bailout loans, granted in return for a harsh austerity program.
Another positive sign came from Italy, which raised $9.9 billion in a bond auction Monday, although the rates it had to pay investors rose slightly.
Wall Street stocks closed mostly lower Monday. The Dow Jones industrial average closed down 0.3 percent at 13,169.43. The Standard & Poor's 500 index declined 0.1 percent to 1,404.11, while the Nasdaq composite rose 0.1 percent to 3,022.52.
Benchmark oil for September delivery rose 7 cents to $92.80 per barrel in electronic trading on the New York Mercantile Exchange. The contract fell 14 cents to finish at $92.73 per barrel in New York on Monday.
In currency trading, the euro rose to $1.2343 from $1.2336 late Monday in New York. The dollar fell to 78.41 yen from 78.43 yen.