Forex traders said the local currency was trading in a narrow range amid rising risk-aversion in the broader financial markets.
At the interbank foreign exchange, the rupee opened at 75.51, but pared initial gains, and finally settled for the day at 75.58 - lower by just 2 paise over its previous close.
During the trading session, the rupee witnessed an intra-day high of 75.45 and a low of 75.59 against the greenback.
On Thursday, the rupee had settled 10 paise lower at 75.56 against the US dollar.
Finance Minister Nirmala Sitharaman will announce the next tranche of the stimulus package later in the day.
Forex traders said market participants are concerned about the implications of the Rs 20-lakh-crore economic stimulus package on the fiscal deficit, as there is still no clarity on how the package would be financed.
Meanwhile, domestic bourses were trading on a muted note with the benchmark Sensex quoting 14.39 points higher at 31,137.28 and the broader Nifty up 9.05 points at 9,151.80.
Foreign institutional investors were net sellers in the capital market, as they sold equity shares worth Rs 2,152.52 crore on Thursday, according to provisional exchange data. DRR ANSANS