Japan's benchmark Nikkei 225 stock average rose 0.5 percent to 10,548.09, while South Korea's Kospi jumped 1.5 percent to 1,958.52.

Shares in Singapore and New Zealand were also higher, as well as shares in Hong Kong and mainland China.

Australia's S&P/ASX 200 index was an exception, slipping less than 1 percent to 4,801.20.

The mostly strong showing followed gains in the U.S. A strong report on hiring by a payroll company surprised investors and gave hope the dark clouds over the job market may be clearing, though concerns remained over Libya's internal conflict and the recent rise in oil prices.

Payroll processor ADP said U.S. private companies added 217,000 jobs in February, well above the 180,000 analysts had predicted. Analysts said that sets a positive tone for a U.S. government jobs report for February due out on Friday.

The Dow Jones industrial average rose 0.1 percent to close at 12,066.80, while the broader S&P 500 rose 0.2 percent to 1,308.44. Both indexes fluttered between gains and losses throughout the day.

Investors are still worried that the recent wave of uprisings in the Middle East could spread and lead to interruptions in the global flow of oil.

In currencies, the dollar rose to 81.86 yen from 81.84 yen overnight, while the euro fell to $1.3857 from $1.3863.