Buying sentiment was also boosted by a rally on Wall Street, while Japanese traders were still on a high after Tokyo’s successful bid to host the Olympic Games in 2020.
Tokyo was up 1.54 percent, or 218.13 points, at 14,423.36, adding to its 2.48 percent rise on Monday as Olympic-related firms enjoyed further buying.
Sydney advanced 0.38 percent, or 19.7 points, to close at 5,201.2, while Seoul added 0.98 percent, or 19.39 points, to 1,994.06.
Shanghai rose 1.15 percent, or 25.47 points, to 2,237.98, boosted by news that industrial production in China had expanded in August at its fastest rate in more than a year. Hong Kong climbed 0.99 percent, or 226.00 points to 22,976.65.
The gains follow strong trade figures Monday and add to recent results pointing to a pick-up in the world’s number two economy and key driver of global growth.
Also Monday Japan said its economy expanded at a faster pace in the April-June quarter than originally estimated, fueling hopes that years of anemic growth could be coming to an end.
The positive numbers follow last week’s figures on manufacturing from China, Europe and the United States that all pointed to an increase in activity.
“Prospects for a global economic rebound have allowed for more confidence in equities markets, which has made the upside direction clearer,” SMBC Nikko Securities general manager of equities Hiroichi Nishi told Dow Jones Newswires.
Investors also welcomed a possible breakthrough in the Syria crisis after Russia proposed a plan to avert a US-led strike on Damascus by securing a deal for the regime to destroy its chemical weapons.
US President Barack Obama said the move could be a “significant breakthrough,” easing concerns of an attack that many analysts fear could lead to a wider conflict in the Middle East.
Wall Street welcomed the latest events. The Dow rose 0.94 percent, the S&P 500 increased 1 percent and the Nasdaq climbed 1.26 percent.
Oil prices retreated as supply worries softened. New York’s main contract, West Texas Intermediate for delivery in October, fell $1.02 to $108.50 in afternoon trade, while Brent North Sea crude for October was 80 cents lower at $112.92.
In currency trade the dollar bought 100.05 yen, compared with 99.69 yen in New York on Monday.
The euro fetched 132.54 yen compared with 132.10 yen while it was at $1.3247 from $1.3254.
There were also advances in emerging markets as a weaker-than-expected US jobs report on Friday tempered expectations the Federal Reserve will start to wind down its stimulus program this month.
Mumbai, which was closed for a public holiday Monday, closed 3.77 percent higher, Jakarta added 3.98 percent and Manila ended up 1.54 percent, or 92.68 points, at 6,089.72.
Developing nations around the world slumped last month on fears of an end to the Fed’s bond-buying, which has been credited with fuelling an investment splurge in their economies since over the past year.
Gold cost $1,372.04 an ounce at 1100 GMT compared with $1,385.42 late Monday.
In other markets:
— Bangkok added 0.64 percent, or 8.86 points, to 1,393.17.
Department store operator Central Pattana jumped 5.77 percent to 41.25 baht, while coal producer Banpu dropped 4.49 percent to 298 baht.
— Kuala Lumpur rose 1.03 percent, or 17.92 points, to 1764.95.
Property developer UEM Sunrise, which rose 6.3 percent to 2.52 ringgit, and SapuraKencana Petroleum, which climbed 2.8 percent to 3.70 ringgit.
— Singapore closed up 1.16 percent, or 35.69 points, at 3,123.89.
Singapore Telecom rose 1.13 percent to Sg$3.59 and real estate developer Capitaland gained 0.66 percent to Sg$3.04.
— Taipei rose 0.20 percent, or 16.66 points, to 8,208.77.
Taiwan Semiconductor Manufacturing Co. was 1.46 percent higher at Tw$104.5 while smartphone maker HTC surged 5.16 percent to Tw$132.5.
— Wellington rose 0.30 percent, or 13.74 points, to 4,627.75.
Telecom added 1.36 percent to NZ$2.23 and Fletcher Building advanced 1.18 percent to NZ$9.42.—Danny McCord