Meanwhile, the U.S. faced diplomatic pressure to await a United Nations report due later this week before taking action against Syria for the suspected use of chemical weapons. Obama will appear in several television interviews this week as he tries to persuade members of Congress to vote for a military strike.
(Read more: Syria will fan flames of Sept. volatility)
Shanghai rallies 3.4%
China's benchmark index crossed the 2,200 mark to hit its highest level since June 7 after a spate of recent data confirmed hopes that China's economy is stabilizing.
Annual consumer inflation rose 2.6 percent in August, matching expectations and little changed from the previous month while producer prices fell 1.6 percent in August, compared to July's 2.3 percent drop. The data follows August trade figures released over the weekend, which showed the country's exports rose a higher-than-expected 7.2 percent from a year ago.
Banks rallied with Pudong Development Bank, Bank of Communications, and Agricultural Bank of China up by their maximum daily limit of 10 percent.
(Read more: China's economy coming up trumps)
"Either you're a believer in China or a disbeliever. Even if you're a believer, you still have to sell the stocks you want to buy, because the good companies are very expensive and the lousy companies are so questionable that you shouldn't touch them to start with. I would rather buy Hong Kong shares or Macau casino stocks," said Marc Faber, publisher of The Gloom, Boom & Doom Report.
Nikkei up 2.5%
Japanese stocks rose above the 14,160 mark to hit a new one-month high on the back of positive economic reports.
Revised gross-domestic-product (GDP) data for April-June showed the economy grew 0.9 percent from the previous quarter, topping expectations for a 0.6 percent rise, while revised capital expenditure shot up 1.3 percent in the same period, the first rise in six quarters.