The partially convertible rupee erased the previous session's losses, strengthening 0.21 percent to close at 45.065/075 per dollar. It had ended Monday at 45.16/17.
"The fact that stocks gained today also helped," a trader at a state-run bank said. "With the euro now eyeing a possible ECB rate hike, we could see the rupee gaining past 45 tomorrow."
In European trade, the single currency erased early losses and gained ground against the dollar after data showing Germany's Ifo business climate index at a five-year high in October fanned talk of rate rises in Europe.
Earlier, the Reserve Bank of India raised its short-term reverse repo rate by a quarter of a percentage point to 5.25 percent to ward off price pressures, and increased its growth forecast for one of the world's fastest expanding economies.
The Indian central bank said it expected Asia's third-largest economy to grow 7.0-7.5 percent in the fiscal year to March 2006, having forecast in April that growth would be around 7.0 percent.