At 0235 GMT, the MSCI's index of Asia Pacific shares outside Japan was up 1 percent, while the Nifty India futures traded in Singapore were 0.6 percent higher suggesting a firm open to the local market.
The euro recovered from a dip to one-week lows in Asia on Wednesday, with markets cautiously optimistic that recent credit warnings by Standard & Poor's would spur European leaders into more decisive action at this week's summit.
Traders said the central bank's assurance that it would prevent the rupee from falling sharply by intervening in the forex market would also underpin the market sentiment.
Traders forecast the rupee to open around 51.20 per dollar and move in a range of 51.10 to 51.50. It had ended 0.4 percent weaker on Monday at 51.41/42 and the market was closed on Tuesday for a local holiday.
The index of the dollar against six major currencies was down 0.1 percent at 78.439 points. It had been at 78.483 points when the rupee market closed on Monday. The euro was trading at $1.3423 versus $1.3433 previously.