At the interbank forex market, the local unit opened lower at 80.00 against the greenback and fell further to an intra-day low of 80.05.
On Monday, foreign institutional investors were net sellers in the capital market as they sold shares worth Rs 170.51 crore, as per exchange data.
The dollar index marked the first weekly decline after six weeks of upward movement, driven by position liquidation and preference for other currencies to emerge at a lower level.
The rupee finally closed at 76.43, registering a rise of 18 paise over its previous close.
At the interbank forex market, the local unit opened at 76.40 against the greenback and witnessed an intra-day high of 76.19 and a low of 76.44.