The rupee appreciated 29 paise to close at 75.66 against the US dollar on Tuesday tracking weakness in the American currency, while easing of COVID-19 lockdown measures fuelled growth optimism.
At the interbank foreign exchange, the rupee opened at 75.69, then gained ground and finally settled for the day at 75.66, registering a rise of 29 paise over its previous close.
On Friday, Rupee had settled at 75.95 against the US dollar.
Forex market was closed on Monday for Id-Ul-Fitr.
During the trading session, the rupee witnessed an intra-day high of 75.62 and a low of 75.74.
Forex traders said the weakness of the US dollar against other currencies overseas and easing of lockdown restriction across the world boosted investor sentiment and supported the local unit.
In the equity market, domestic bourses pared initial gains and were trading on a negative note with the benchmark Sensex down 151.66 points at 30,520.93 and broader Nifty 41.65 points lower at 8,997.60.
The dollar index, which gauges the greenback's strength against a basket of six currencies, was trading 0.44 per cent down at 99.42.
Meanwhile, foreign institutional investors were net sellers in the capital market, as they sold equity shares worth Rs 1,353.90 crore on Friday, according to provisional exchange data.