At 10:45 a.m. (0515 GMT), the partially convertible rupee was at 44.2925/2975 per dollar, 0.1 percent stronger than its previous close of 44.325/335.

"I expect the dollar inflows to continue and the rupee is likely to appreciate further this week," said N.S.S. Mani, chief dealer at State Bank of Travancore.

"Today, I see the rupee in a range of 44.20-44.40 with an upward bias," he said.

Indian shares rose more than 1 percent tracking firm Asian peers and supported by increasing demand from foreign portfolio investors.

Traders said the dollar's rise overseas could temper the rupee's gains.

The index of the dollar against six major currencies was up 0.23 percent at 74.993 points. The index was at 74.763 points when the rupee market closed on Friday.

The euro extended its losses on Monday after repeated attempts to break above a resistance level failed yet again and on renewed worries about euro zone debt problems, giving the dollar a much needed reprieve after the recent sell-off.

The one-month onshore forward premium was at 26.00 basis points versus its previous close of 25.75. The three-month was at 83.50 basis points versus 82.75 and the one-year was at 321.25 basis points compared with 309.

The one-month offshore non-deliverable forward contracts were quoted at 45, weaker than the onshore spot rate.

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 44.3675, with total volume at $1.52 billion.