At 11:21 a.m., (0551 GMT) the partially convertible rupee was at 49.1950/2025 per dollar, 0.5 percent stronger than its Monday's close of 49.445/455. It has traded in a 49.14-49.30 band so far in the day.
"Its essentially news driven action. Overnight there has been some positive news on the euro front, which has strengthened the rupee," said a dealer with a state-run bank.
"So again if some bad news comes, we will see rupee going past 49.50."
Euro zone officials are working to magnify the firepower of the region's rescue fund, European Central Bank policymakers said on Monday, while US President Barack Obama piled on pressure for Europe to staunch a sovereign debt crisis that threatens the world economy.
Traders expect the rupee to move in a 49.00-49.40 band intraday and said dollar demand from oil importer could limit the rupee's gains.
Oil is India's largest import item and oil refiners are the largest buyers of dollars in the local market.
Brent crude rose above $105 as concerns over Europe's debt crisis eased temporarily and a weaker US dollar sparked buying of dollar-denominated assets.
Indian shares rose 2 percent in morning trade on Tuesday, and most Asian currencies were also stronger against the dollar.
The euro crawled up from eight-month lows as a report that Europe is considering beefing up its bailout fund prompted short-covering, and it could extend its rebound in the very near term given traders' overwhelmingly short positions in the currency.
The euro was at $1.3549, compared with $1.3523 when the rupee closed on Monday, while the index of the dollar against six major currencies was at 77.922 points against 78.029.
The one-month onshore forward premium was at 22 points from 21.25 on Monday, the three-month was at 65 points from 64.50 and the one-year was steady at 127 points.
The one-month offshore non-deliverable forward contracts were quoted at 49.46, weaker than the onshore spot rate, suggesting a bearish near-term outlook.
In the currency futures market , the most traded near-month dollar-rupee contracts on the National Stock Exchange, the MCX-SX and the United Stock Exchange were all at 49.2150. The total traded volume on the three exchanges was $2.7 billion.