Japan's benchmark Nikkei 225 stock average added 30.50 points, or 0.3 percent, to 9,469.63 in the morning session.
The Nikkei held firm as the government said Japan's economy - the world's second-largest - grew a revised 5.0 percent in the January-March quarter, up from an earlier estimate of 4.9 percent growth.
Big losers in Tokyo included major trading house Mitsui & Co. Ltd, whose shares plunged 7.3 percent to close the morning session at 1,081 yen. A Mitsui unit - Mitsui Oil Exploration Co. Ltd. - owns a 10 percent stake in the well where the leak occurred.
Mitsui Oil Exploration is not listed on the stock exchange.
South Korea's Kospi index slipped 0.33 points to 1,646.89, while Australia's S&P/ASX 200 was up 0.9 percent at 4,442.20.
Hong Kong's Hang Seng fell 0.5 percent to 19,517.61. Benchmarks in mainland China declined, but shares in Singapore and Taiwan rose marginally.
In New York Wednesday, the Dow Jones industrial average fell 40.73 points, or 0.4 percent, to 9,899.25. While the Dow gained more than 125 points at midday, it slumped later as investors sold energy stocks on fears that the U.S. oil spill disaster could force BP to seek bankruptcy protection.
Across Asia, investors were cautious amid lingering concern over Europe's fiscal crisis and its impact on a global economic recovery.
In currencies, the dollar declined to 91.19 yen in Tokyo Thursday from 91.26 yen in New York late Wednesday. The euro slipped to $1.1970 from $1.1980.
Benchmark crude for July delivery rose $2.55 to $74.54 a barrel on the New York Mercantile Exchange.