"Hopes that European politicians have a good understanding on the potential need to recapitalize the banking system has been key support to risk appetite in recent sessions," said Jane Foley, an analyst at Rabobank International. "The very nature of the political process is slow, however, suggesting that once again there is room for disappointment and volatility in the markets."
Earlier in Asia, Japan's Nikkei index rose 1% to close at 8,605.62 after the country's central bank said the economy is "picking up" and predicted an eventual return to a moderate recovery.
South Korea's Kospi index jumped 2.9% to close at 1,759.77 and Hong Kong's Hang Seng ended 3.1% higher at 17,707 after surging 5.7% the day before.
Markets in mainland China were closed for a weeklong holiday.Oil prices tracked equities lower -- benchmark crude oil for November delivery was down 55 cents to $82.94.