The rupee gained 33 paise to touch 81.77 against the US dollar during early trade on Monday, July 3. The rupee had closed at 82.1 against the US dollar on Friday, June 30.

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The dollar index — which measures the American currency against the yen, the pound, the Canadian dollar, the Swedish krona, the Swiss franc and the euro — was last trading nearly 0.2 percent higher at 102.782.

Crude oil benchmarks were trading lower today. At the last count, Brent crude futures were trading 0.16 percent down at $75.29 per barrel. WTI futures, too, were trading 0.2 percent lower at $70.50 per barrel.

There has been "massive (dollar) selling" by foreign banks since open, a proprietary trader at a private sector bank said. There was talk of debt inflow related to a large conglomerate, and then "there are the usual equity inflows," the trader added.

Price action suggested that RBI may be there, another trader said. "But then... there will anyway be decent buying interest at these levels from importers."

Both, Indian benchmark indexes Sensex and Nifty50, were trading around 0.6 percent higher around 12.30pm.

With inputs from Reuters

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