This is the second consecutive day of gain for the rupee, during which it has appreciated by 28 paise.
At the interbank foreign exchange, the rupee opened at 76.33. During the session it touched an intra-day high of 76.14 and a low of 76.44.
The domestic unit finally settled at 76.18, registering a rise of 7 paise over its previous close.
On Monday, the local unit had settled at 76.25 against the US dollar.
Meanwhile, domestic stock exchanges were trading on a positive note with benchmark indices Sensex trading 330.07 points higher at 32,073.15 and Nifty up by 89.05 points at 9,371.35.
The dollar index, which gauges the greenback's strength against a basket of six currencies was trading 0.20 per cent down at 99.84.
"Today is the USD/INR April contract expiry on exchange. This April contract had been trading 40p above OTC and though a lot of longs have been rolled over, the Open Interest in the April contract is still USD 2bn. We may see buying at RBI fix today in OTC as positions get squared off on exchange," said Abhishek Goenka, Founder and CEO, IFA Global.