The rupee depreciated by 6 paise to close at 71.18 against the US dollar on Monday amid muted activity in domestic equities and steady rise in crude oil prices.
Forex traders said the rupee is trading in a narrow range amid lack of cues from the global market.
At the interbank foreign exchange market, the domestic currency opened weak at 71.15 and later fluctuated between a high of 71.11 and a low of 71.24.
The domestic unit finally settled at 71.18, showing a fall of 6 paise over its previous close of 71.12 on Friday.
"Rupee failed to witness any trend and continued to quote in a narrow range of 71.05 to 71.25 (spot) due to lack of cues from domestic as well as global front," said Gaurang Somaiyaa, Forex & Bullion Analyst, Motilal Oswal Financial Services.
Somaiyaa further said volatility would be low for the currency as no economic data is expected in this week. Moreover, this week is a relatively shorter week as market participants remain on the sidelines following Christmas holidays.
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Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, rose by 0.01 per cent to 97.69.
"Rupee has been trading in a narrow range as there is absence of renewed triggers in the worldwide cues. Hence a tight range bound trading is observed as both importers and exporters wait for cues or better level to hedge the positions," said Jateen Trivedi, Senior Research Analyst (Commodity & Currency) at LKP Securities.
On the domestic market front, the 30-share BSE Sensex settled 38.88 points, or 0.09 per cent, down at 41,642.66, while the broader NSE Nifty slipped 9.05 points, or 0.07 per cent, to close at 12,262.75.
Foreign institutional investors (FIIs) remained net buyers in equities, as they purchased shares worth Rs 338.86 crore on a net basis on Friday, according to provisional exchange data.
Brent futures rose 0.03 per cent to USD 66.16 per barrel.
The 10-year government bond yield was at 6.56 per cent.
The Financial Benchmark India Private Ltd (FBIL) set the reference rate for the rupee/dollar at 71.1569 and for rupee/euro at 79.1051. The reference rate for rupee/British pound was fixed at 92.6164 and for rupee/100 Japanese yen at 65.09.