"Equities are currently set to hold onto yesterday's bumper gains after a solid close on Wall Street as investors continued to cheer the U.S. bail out plan for financial giant Citigroup," said Matt Buckland, a dealer at CMC Markets.
Earlier, Asian markets broke higher despite muted gains Monday to the Citigroup news. But after seeing markets in Europe and the U.S. surge Monday, Asian investors joined in the rally.
In Japan, which had been on holiday Monday, the Nikkei 225 stock average soared 413.14 points, or 5.2 percent, to 8,323.93. Hong Kong's Hang Seng index rose 3.4 percent to 12,878.60.
Wall Street and European markets were buoyed Monday by the news that the U.S. government will take a $20 billion stake in Citigroup and guarantee hundreds of billions of dollars in risky assets. In addition, hints from President-elect Barack Obama that he will introduce a massive fiscal stimulus package once he is in the White House in January helped markets rally.
The Dow Jones industrials soared 396.97 points, or 4.9 percent, to 8,443.39 Monday - the first two-day advance since Oct. 31.
"Global equity markets have heaved a sigh of relief courtesy of the weekend's salvation of Citigroup and Obama's fiscal plans," said Neil Mellor, an analyst at Bank of New York Mellon.
Despite the relief in stock markets, Mellor is skeptical that stock markets have bottomed out.
"There is scant evidence that this moment has arrived," he said, noting ongoing downgrades in economic growth projections and mounting fears of possible deflation.
U.S. stock index futures indicated that there would likely be some profit-taking at the opening bell. Dow futures were down 52 points, or 0.7 percent, at 8,327, while Standard & Poor's futures were down 5 points, or 0.6 percent, at 843.
All eyes will be on a raft of data releases in the U.S. over the coming two days before the Thanksgiving Day holiday on Thursday. The likely most important release Tuesday is the latest estimate of third quarter U.S. gross domestic product.
"A raft of numbers out of the U.S. will be closely watched as the Dow has posted the best part of a 1,000 point gain over the last two trading days and traders will now inevitably be looking for a signal to book profits," said CMC's Buckland.
Elsewhere in Asia, Australia's benchmark S&P/ASX200 index leaped 5.8 percent to close at 3,623.4, led by materials, energy, banks and consumer discretionary stocks.
The main development in Asia was the news that BHP Billiton Ltd., the world's biggest mining company, has abandoned a hostile $68 billion takeover bid for rival Rio Tinto Ltd., blaming the global economic downturn and plunging commodity prices.
Shares of BHP Billiton rose 12.5 percent to 1,102 pence in London trading, where both companies are traded in addition to Australia. Rio Tinto shares plunged almost 40 percent to 1,489 pence.
The Philippines' main index jumped more than 6 percent. Among other major markets, mainland China, Singapore and India declined.
Chinese stocks have rolled back since rallying earlier this month on news of a multibillion dollar government economic stimulus package. Adding to concerns, the World Bank on Tuesday cut its 2009 growth forecast for China from 9.2 percent to 7.5 percent - the lowest rate in 18 years.
After jumping $4.57 overnight, light, sweet crude for January delivery was down $2.37 to $52.13 a barrel in electronic trading on the New York Mercantile Exchange by late-morning London time.
In currencies, the dollar fell 1.4 percent to 95.73 yen while the euro slid 0.7 percent to $1.2826.
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Associated Press writers Tomoko A. Hosaka in Tokyo and Jeremiah Marquez in Hong Kong contributed to this report.
