Prospects for U.S. trading appeared muted, with Dow and S&P 500 futures both down 0.1 percent.
But expectations that U.S. Federal Reserve Chair Janet Yellen will stick to a stance of keeping interest rates low during testimony in Congress this week is helping support sentiment despite the Fed's plans to gradually scale back its asset purchases.
China, the world's No. 2 economy, is due to report its second quarter GDP on Wednesday. Premier Li Keqiang raised hopes for an upbeat outcome by commenting last week that growth improved from 7.4 percent in the first quarter.
Japan's Nikkei 225 added 0.6 percent to 15,395.16 after a central bank policy meeting ended as expected with no changes to Tokyo's ultra-loose monetary policy.
Hong Kong's Hang Seng gained 0.5 percent to 23,459.96 and South Korea's Kospi rose 0.9 percent to 2,012.72.
Australia's S&P/ASX 200 was little changed at 5,511 after being weighed down by a drop in gold prices and weakness in banks and manufacturing companies. Shares in Thailand and Singapore also fell, while most other regional markets were higher.
Benchmark U.S. crude for August delivery slipped 17 cents to $100.74 per barrel in electronic trading on the New York Mercantile Exchange. The contract slipped 8 cents to close at $100.91 on Monday on expectations of higher supplies and muted global demand.
In currency markets, the dollar fell to 101.53 yen from 101.57 yen late Monday. The euro dropped to $1.3604 from $1.3623.