The dollar bided well after the market started pricing a full percentage point hike at next week's Federal Open Market Committee (FOMC) meeting.
"However, the recovery in domestic equities and corporate dollar supply gave support to the rupee after a weak opening," Parmar said, adding that in the near term, the spot USDINR is expected to trade in the range of 79.65 to 78.70.
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, was trading 0.35 per cent lower at 109.43.
Brent crude futures, the global oil benchmark, advanced by 0.62 per cent to USD 93.75 per barrel.
On the domestic equity market front, the BSE Sensex ended 224.11 points or 0.37 per cent lower at 60,346.97, while the broader NSE Nifty declined 66.30 points or 0.37 per cent to 18,003.75.
Foreign institutional investors were net buyers in the capital market on Tuesday as they purchased shares worth Rs 1,956.98 crore, as per exchange data.