Tokyo's Nikkei Index was up 1.03 per cent late morning, Hong Kong was 0.65 per cent higher and Shanghai had risen 0.27 per cent. Sydney's S&P/ASX 200 dipped by 0.3 per cent.
On Tuesday Saudi Arabia moved to ease fears about surging world oil prices, which have hit two-and-a-half-year highs in recent days due to the crisis in Libya and fears of regional instability, with some analysts fretting that Saudi could itself see a rise in unrest.
Oil Minister Ali Naimi said his country's spare capacity was able to make up any supply shortfalls and the kingdom was also developing a "special mix" of oil that resembles Libya's light sweet crude.
"Current supplies in the market are very adequate, and there is an extra output capacity that could be used if needed," the state SPA news agency quoted him as saying.
Wall Street was buoyed by the minister's words and an indication of more upbeat small-business sentiment in a report by the National Federation of Independent Business.
The Dow Jones Industrial Average surged 1.03 per cent, the S&P 500 index rose 0.89 per cent and the tech-rich Nasdaq Composite climbed 0.73 per cent.
Signalling improved sentiment generally, the value of safe-haven gold dipped, after striking a new all-time record high of $1,440.32 in London on Monday.
Gold opened at $1,427.00-$1,428.00 an ounce in Hong Kong, a shade down from Tuesday's close of $1,428.00-$1,429.00.
Among Asian markets, Shanghai's Composite Index was extending a three-session rise after investors were calmed by assurances from officials that suggested further interest rate hikes were not imminent.
Also helping was a pledge by the State Administration of Grain to increase the country's grain supply to help keep prices stable.
Chinese banks particularly advanced on hopes of solid full-year earnings, while in Hong Kong, Cathay Pacific shares were up ahead of the airline's full year results later in the day.
On Asian currency markets the dollar rose against the euro as oil prices eased and worries increased about eurozone debt problems.
The euro retreated to $1.3887 in Tokyo morning trade from 1.3905 in New York late Tuesday. The single European currency rose to 115.02 yen from 114.91 yen.
The dollar firmed to 82.83 yen from 82.64 yen.
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