The rupee opened higher at 64.14 against yesterday's closing of 64.16 at Interbank Foreign Exchange market and hovered in a range of 64.12 and 63.89 before finishing at 63.91, showing a gain of 25 paise or 0.39 per cent.
It had dropped by 61 paise, or 0.96 per cent, in previous four trading days.
Foreign portfolio investors sold shares worth a net Rs 859.94 crore on Monday, as per provisional data released by the stock exchanges.
In the overseas market, the dollar advanced against the yen on Tuesday as worries about China's stock sell-off abated somewhat, but the buck fell against the pound after the latest reading on UK economic growth matched expectations.
Some stabilisation in Asian stocks prompted nervous investors to loosen their grip on the perceived safety of the Japanese currency.
The benchmark BSE Sensex dropped further by 102.15 points, or 0.37 per cent, to settle at 27,459.23.
Meanwhile, a two-day policy meeting of the Federal Reserve Open Market Committee begins on Tuesday.
The US central bank is widely expected to keep interest rates at a record low at the meeting, but expectations are rising that a rate hike could come later this year.
The dollar index was trading higher by 0.36 per cent against its major global rivals on Tuesday.
Veracity Group CEO Pramit Brahmbhatt said, "Rupee traded strong against the dollar ahead of the Reserve Bank's policy review which is due for next week."
Though weak closing of local equities limited the rupee's gain, strong dollar index further troubled the local currency and restricted its movement.
The trading range for the Spot USD/INR pair is expected to be within 63.60 and 64.20.
In the forward market, the premium for dollar declined on sustained receiving from exporters.
The benchmark six-month premium payable in December moved down further to 197.25-192.75 paise from 193.25-194.25 paise yesterday while far-forward contracts maturing in June, 2016 also eased to 421-423 paise from 421.5-423.5 paise.
The RBI fixed the reference rate for the dollar at 64.0270 and for the euro at 70.8843.
The rupee fell further against the pound sterling to end at 99.63 from 99.55 yesterday but firmed up against the euro to 70.51 from 71.03 in the previous session.
The local unit recovered against the Japanese currency at 51.65 per 100 yen from 52.05 in last session.