The U.S. Labor Department said employers posted the most job openings in four years in June, a positive sign that hiring in the world's largest economy may pick up. That follows Friday's report that U.S. employers in July added the most jobs in five months, far more than economists were expecting.
The positive jobs news out of the U.S. added to optimism that investors have been feeling for much of the past few weeks, largely on hopes that the European Central Bank will play a more pivotal role in Europe's debt crisis.
Japan's Nikkei 225 index rose 1.4 percent to 8,922.36. South Korea's Kospi added 1.3 percent to 1,911.17, as sentiment improved a day ahead of a Bank of Korea meeting where policy makers are expected to lower interest rates to stimulate the economy.
Australia's S&P/ASX 200 rose 0.6 percent to 4,316. Benchmarks in Taiwan, Indonesia and Thailand also rose.
But Hong Kong's Hang Seng index fell 0.2 percent to 20,036.56 as investors became cautious ahead of the release of key inflation, industrial production and retail sales data out of China on Thursday.
Hong Kong-listed property stocks sagged following reports in local media quoting the government as reiterating its willingness to impose restrictions.
"They don't want to see a property bubble re-emerge," said Andrew Sullivan, principal sales trader at Piper Jaffray in Hong kong. Mainland Chinese shares also fell.
Shares of troubled clothing chain Esprit Holdings Ltd. Plunged 11 percent as investors took profits a day after the stock leapt by nearly a third on news it was hiring a new CEO from Spain's Inditex, owner of the popular Zara brand. Separately, Macau casino operator MGM China Holdings Ltd. rose 4.1 percent after it said revenue in the world's biggest gambling market for the latest quarter rose 6 percent.
Gains among European stocks Tuesday were largely due to hopes the ECB will soon start buying the bonds of Spain and Italy and a hint from Spanish Prime Minister Mariano Rajoy that he could request a financial bailout for his country.
Spain has seen the yield on its benchmark 10-year bonds fall below the 7 percent level considered unsustainable in the long-run. It was at 6.80 percent at the end of trading Tuesday, a sign of confidence in the Spanish economy.
"The near-term outlook for risk assets has improved following stronger-than-expected US July payrolls and hints from Spain's Prime Minister Rajoy that he's willing, at last, to consider applying for full assistance from the EU," Stan Shamu of IG Markets in Melbourne said in a market commentary.
Stocks on Wall Street jumped Tuesday thanks in part to strong corporate earnings. The Dow Jones industrial average rose 0.4 percent to close at 13,168.60. The Standard & Poor's 500 rose 0.5 percent to 1,401.35. The Nasdaq composite index rose 0.9 percent to 3,015.86.
Meanwhile, recent comments by Federal Reserve chairman Ben Bernanke that the slow economic recovery has hurt many Americans has kept hope alive that the Fed will take more steps to kick-start the economy at its next meeting in September.
Benchmark crude for September delivery fell 37 cents to $93.30 a barrel in electronic trading on the New York Mercantile Exchange. The contract rose $1.47 to finish at $93.67 per barrel on the Nymex on Tuesday.
In currencies, the euro fell to $1.2393 from $1.2410 late Tuesday in New York. The dollar fell to 78.50 yen from 78.65 yen.