Dollar sales by banks and exporters and foreign capital inflows into the equity market supported the rupee.
The rupee resumed higher at 62.35 per dollar from the previous close of 62.44 on the interbank foreign exchange market and firmed up to 61.96, a two-week high.
The currency failed to maintain the gains on dollar demand from importers, mainly oil refiners, and ended at 62.31 per dollar, a rise of 0.20 per cent.
"Rupee started its weak trend as RBI announced that the oil marketing companies have started accessing the forex market for their dollar demand. This return of OMCs to the market is likely to put pressure on the rupee," said Abhishek Goenka, CEO of India Forex Advisors.
The Reserve Bank of India said state-run oil refiners returned to the foreign exchange market last week to meet all their dollar requirements. A swap window, which had been made available to the refiners since August end, will open on rare days, when there is a pronounced spurt in dollar demand, the central bank said.
The RBI also said USD 34 billion was mobilised from special concessional dollar swap windows opened in September for deposits by non-resident Indians and overseas foreign currency borrowings by banks. The swap windows were closed on November 30.
India's current account deficit narrowed to USD 5.2 billion, or 1.2 per cent of GDP, in the July-September quarter after a turnaround in exports and a decline in gold imports, the RBI said after the market closed.
The gap between the outflow and inflow of foreign exchange was USD 21 billion, or 5 per cent of GDP, in the second quarter of the previous financial year.
The dollar index, which measures the US currency's value against a basket of six major currencies, was trading positively, which capped the rupee's gain, said Pramit Brahmbhatt, CEO of Alpari Financial Services (India).
The 30-share Indian benchmark Sensex rose 106 points, or 0.51 per cent, to 20,898.01. Overseas investors bought a net Rs 745.16 crore of shares on Friday, according to provisional stock exchange data.
In the forward market, the dollar premium declined further due to sustained receipts from exporters.
The benchmark six-month forward dollar premium payable in April dropped further to 213-214 paise from 218-220 paise previously and far-forward contracts maturing in October dipped to 447-449 paise from 453-1/2-455-1/2 paise.
The RBI fixed the reference rate for the dollar at 62.2260 and for the euro at 84.6410.
The rupee declined to 102.06 against the pound from 101.98 on Friday and firmed up to 84.31 against the euro from 84.98 previously.
The rupee hardened to 60.64 per 100 Japanese yen from 61.02 previously.