The domestic currency resumed higher at 64.05 a dollar as against the last weekend's level of 64.08 at the interbank foreign exchange market and firmed up further to a high of 63.99 on initial selling of dollars on hopes of more foreign funds into equities.
However, it dropped afterwards to 64.14 before ending at 64.13 per dollar, showing a loss of 5 paise or 0.08 per cent.
The rupee had gained by four paise, or 0.06 per cent, against the dollar on last Friday.
In cross-currency trades, the rupee ended higher against the pound sterling at 86.86 as against the previous closing of 87.03 per pound but fell against the euro to finish at 76.71 from 76.59 in the previous trade.
The domestic unit also weakened against the Japanese yen to settle at 57.67 per 100 yens from 57.58 in the previous trade.
The RBI, meanwhile, fixed the reference rate for the dollar at 64.0371 and for the euro at 76.4923.
Overseas, the dollar held firm near a seven-week high versus the yen in the early trade today, supported by recent rises in US yields, while pound sterling took a breather after surging last week on growing expectations that the Bank of England could raise interest rates soon.
The dollar advanced in the late global trade, particularly rallying against the yen as concerns over North Korea abated and traders looked ahead to the Federal Reserve meeting later in the week.
However, the dollar index against a basket of six major currencies was trading down by 0.02 per cent in the late afternoon trade.
Meanwhile, foreign portfolio investors (FPIs) bought shares worth Rs 418.86 crore last Friday, as per provisional data released by the stock exchanges.
The Indian benchmark Sensex rose further by 151.15 points, or 0.47 per cent, to end at 32,423.76.
In forward market, today, premium for dollar declined further on sustained receiving’s from exporters.
The benchmark six-month premium payable in February eased further to 119-121 paise from 120.25-122.25 paise on last Friday and the far forward August 2018 contract also moved down to 260-262 paise from 260.50-262.50 paise.
In global market, oil futures turned moderately lower today, failing to hold on to early gains after prices rose to a five-month high last week, buoyed by recent data showing tightening supplies.
Brent crude, the global oil benchmark, lost 26 cents, or 0.5 per cent, to USD 55.36 a barrel on London's ICE Futures exchange. On the New York, Mercantile Exchange, West Texas Intermediate futures declined 26 cents, or 0.5 per cent, to USD 49.63 a barrel.