At the interbank forex market, the local unit opened at 74.20 against the US dollar, then gained further and touched 74.10, registering a rise of 26 paise over its previous close.
On Wednesday, the rupee had settled at 74.36 against the American currency.
The rupee started on a stronger note against the greenback after the dovish statement by the US Federal Reserve weighed on the greenback, Reliance Securities said in a research note adding that the strength of the equity markets also supported the local unit.
The US Fed kept policy rates and asset purchases unchanged. The Fed acknowledged the pick-up in economic activity and employment.
Meanwhile, the dollar index, which gauges the greenback''s strength against a basket of six currencies, fell 0.03 per cent to 90.58.
The US dollar index was trading weaker this morning in Asian trade as a dovish Fed continued to weigh on the greenback. Markets now could track the release of the US GDP and jobless claims data due later, the Reliance Securities'' note said.
On the domestic equity market front, the 30-share BSE benchmark Sensex was trading 128.26 points or 0.26 per cent higher at 49,862.10, and the broader NSE Nifty advanced 46.35 points or 0.31 per cent higher at 14,910.90.
Brent crude futures, the global oil benchmark, rose 0.40 per cent to USD 67.54 per barrel.
Foreign institutional investors were net buyers in the capital market as they purchased shares worth Rs 766.02 crore on Wednesday, according to exchange data.