India's benchmark Sensex index also had one of the day's highest gains, shooting up 2.7 per cent to 19,785.29 by early afternoon as foreign investors went bargain-hunting to take advantage of the weakened rupee. Indian stocks were trading at their highest level since late July after the new Reserve Bank of India governor Raghuram Rajan outlined new confidence-boosting measures.
"There is a relief rally happening in the Indian markets, said Jagannadham Thunuguntla, head of research for SMC Global Securities Ltd. in New Delhi. "But having said that, it may take considerable amount of time to call it a permanent turnaround."
In early trading in Europe, most indices were also up. The FTSE 100 of leading British shares rose 0.8 per cent at 6,582.48. The CAC-40 in France was trading 1.1 per cent higher at 4,084.22 while Germany's DAX gained 1.5 per cent at 8,397.97.
Wall Street also looked set for gains, with Dow Jones industrial futures rising 0.5 per cent to 15,110. S&P 500 futures rose 0.5 per cent to 1,676.70.
Asian stocks posted solid gains. Tokyo's Nikkei 225, the regional heavyweight, finished 1.5 per cent up to 14,423.36. Hong Kong's Hang Seng index was 1 per cent higher to 22,976.65. China's Shanghai Composite index gained 1.2 per cent at 2,237.98. South Korea's Kospi closed 1 per cent higher to 1,994.06 and Australia's S&P/ASX 200 advanced 0.4 per cent to 5,201.20.
The benchmark in the Philippines ended the day 1.6 per cent up. Indonesia's soared 4 per cent at 4,358.14.
Russian Foreign Minister Sergey Lavrov promised Monday to push Russia's ally Syria to place its chemical weapons under international control and then dismantle them quickly to avert U.S. strikes. Syrian Foreign Minister Walid al-Moallem quickly embraced the proposal.
President Barack Obama has called for military intervention in Syria after alleging that the regime of President Bashar Assad used deadly chemical weapons against civilians in suburban Damascus last month.
Andrew Sullivan at Kim Eng Securities in Hong Kong said markets were boosted by the easing of concerns over Syria in the short term and continuing good data out of Japan and China, Asia's two biggest economies.
"I think generally people are more optimistic," he said, adding that the minutes of the last Bank of Japan meeting released Tuesday morning were also "quite positive."
On Monday, Japanese shares rallied thanks to Tokyo's Olympic bid victory, which helped lift sentiment, while Chinese stocks surged after the economy recorded a bigger-than-expected trade surplus of $28.6 billion in August.
Sullivan said people who have money sitting on the sidelines also are investing as the last quarter of the year rolls in, either in hope of a third quarter rally or in preparation for the first quarter next year.
But there are still a lot of risks out there, he added, including a crucial meeting of the Federal Reserve's policymaking committee next week. The Fed is widely expected to announce plans to start phasing out its support program for the U.S. economy. Meanwhile, the fiscal year ends Sept. 30, and government agencies will start shutting down if some type of budget bill isn't enacted by then.
Benchmark oil for October delivery fell 90 cents to $108.61 per barrel in electronic trading on the New York Mercantile Exchange. The contract fell $1.01 to close at $109.52 a barrel on the Nymex on Monday, spelling good news for shares in Asia, which relies heavily on oil imports.
In currencies, the euro fell to $1.3240 from $1.3251 late Monday. The dollar rose to 100.05 yen from 99.70 yen.
AP business writer Kay Johnson contributed from Mumbai, India.