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.
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.
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.