The rupee weakened by 9 paise to 73.92 against the US dollar in early trade on Tuesday on increased demand for the American currency from banks and importers.
At the Interbank Foreign Exchange, the domestic currency opened higher at 73.79 but lost ground and fell to 73.92.
Dealers attributed the rupee's fall to the dollar's strength against some other currencies overseas but fresh inflows by foreign funds and a higher opening in domestic equity markets, capped the losses.
Moreover, weak exports data also dampened sentiments in the forex market. India's exports entered the negative zone after five months, contracting 2.15 per cent in September to $27.95 billion, according to commerce ministry data.
The rupee had lost 26 paise to close at 73.83 Monday after crude prices rose amid intensifying geopolitical tensions.
The benchmark BSE Sensex on Tuesday rose by 89.17 points, or 0.26 per cent to trade at 34,954.27.
Meanwhile, foreign portfolio investors bought shares worth Rs 67.86 crore on net basis from stock markets on Monday, according to the BSE data.