Investor sentiment improved on Friday as equities continued to rise and foreign funds inflows increased.
FX traders said the greenback was strong in overseas markets, capping local gains.
INR trades at 79.92 against the USD in early deals, up 7 paise from the previous close on the interbank foreign exchange.
Last session, the rupee closed at a record low of 79.99.
A 14-share Nifty rose 82.95 points or 0.52 per cent to 16,021.60, while the 30-share Sensex gained 282.93 points.
Among six currencies, the dollar index gained 0.03 per cent to 108.57.
A barrel of Brent crude futures rose 1.19 percent to USD 100.28.
As per exchange data, foreign institutional investors bought Rs 309 crore worth of shares on Thursday.
A sharp decline in mineral prices led to a three-month low in wholesale price-based inflation in June, but food remained expensive.
May of this year marked a record high of 15.88 percent. As of June 2021, it stood at 12.07 percent.