The Indian rupee ended 51 paise up at 79.45 against the US dollar as heavy short covering was witnessed in capital markets from FIIs, dealers said.
At the interbank foreign exchange market, rupee ended at 79.45 as against 79.96 against US dollar previously.
Indian markets will be closed on Wednesday on account of Ganesh Chaturthi.
"Rupee gained strongly by 0.40 points as heavy short covering was witnessed in capital markets from FIIs. As benchmark rose 2.50 per cent in Indian capital markets, hence rupee time gained more than 0.50 per cent for the first time in the month of August," said Jateen Trivedi, VP Research Analyst at LKP Securities.
Dollar index, which gauges the the strength of greenback against the basket of six major currencies, was at 108.460.
Brent crude oil prices were at $101.49 a barrel by the closing of Indian market hours.
Sensex ended 1,564.45 points, or 2.70 per cent, up at 59,537.07, and Nifty closed 445.40 points, or 2.58 per cent up at 17,759.30. Nifty bank was up sharply 3.29 per cent.
All the 30 stocks on the Sensex ended in green.
"Going ahead, 80.00 will keep acting as strong support for rupee whereas 79.00 will be tested in the coming session," Trivedi added.