The rupee appreciated 8 paise to close at 79.79 (provisional) against the US dollar on Monday, in line with a firm trend in domestic equities.
However, the strengthening of the American currency in the overseas market restricted the rupee's gain, forex dealers said.
At the interbank forex market, the local unit opened at 79.84 against the greenback. It witnessed an intra-day high of 79.79 and a low of 79.90 against the American currency during the session.
It finally ended at 79.79 against the US dollar, up 8 paise from its previous close of 79.87.
The dollar index, which measures the greenback's strength against a basket of six currencies, rose 0.28 per cent to 109.83.
Brent crude futures, the global oil benchmark, rose 2.75 per cent to USD 95.58 per barrel.
"Rupee consolidated in a narrow range despite the dollar rising to a 30-year high. Gains in the dollar extended after non-farm payrolls numbers released from the US came in better-than-estimates," said Gaurang Somaiya, Forex & Bullion Analyst, Motilal Oswal Financial Services.
Euro and pound opened lower as the strength in the dollar continued.
"We expect the USD/INR(Spot) to trade sideways with a positive bias and quote in the range of 79.40 and 80.05," Somaiya said.
On the domestic equity market front, the BSE Sensex ended 442.65 points or 0.75 per cent higher at 59,245.98 points, while the broader NSE Nifty gained 126.35 points or 0.72 per cent to 17,665.80.
Foreign institutional investors were net sellers in the capital market on Friday, offloading shares worth Rs 8.79 crore, as per exchange data.