Domestic currency oscillated within a narrow trading range and struggled for a firm direction as traders preferred to stay near the fence in absence of any fresh trigger.
Most Asian currencies barely budged in thin holiday trade with the Chinese yuan briefly rallying to a 3-1/2-month high before retreating.
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The Indian currency hovered in the range of 64.02-64.11 during the day.
Month-end demand for the greenback from importers and corporates largely outpaced dollar conversions by exporters and inward remittances, a forex dealer said.
Meanwhile, Indian bourses continued their rally with both the benchmark indices closing at fresh life-time highs on fag-end buying in select bluechips.
The BSE benchmark Sensex jumped over 70 points to end at 34,010.61, Nifty rose 39 points to settle at 10,531.50.
Global crude prices traded near 2015 highs on the back of an outlook for healthy demand amid ongoing production cuts led by OPEC and Russia.
Brent crude, an international benchmark, is trading at $65.10 a barrel in early Asian trade. Brent has risen by 47 percent since mid-2017.
In the meantime, overseas investors pulled out a massive Rs 7,300 crore from domestic equity markets this month so far, primarily due to rising crude prices.
At the Interbank Foreign Exchange (forex) market, the home currency resumed mildly positive at 64.03 against last Friday's finish of 64.05 on mild dollar selling by exporters.
Later, it was confined in a narrow trading band of 64.02-64.12 for most part of the day before settling at 64.08, revealing a small loss of 3 paise, or 0.05 per cent.
The rupee had appreciated by 6 paise in the last two days.
The RBI, meanwhile, fixed the reference rate for the dollar at 64.0538 and for the euro at 76.0255.
The dollar index, which measures the greenback's value against a basket of six major currencies, was a tad higher at 92.94 in early trade.
In cross-currency trades, the rupee gained further ground against the pound sterling to close at 85.59 from 85.63 per pound, but fell back modestly against the euro to finish at 75.95 from 75.91 last weekend.
The local unit also retreated against the Japanese yen to end at 56.56 per 100 yens from 56.50.
In forward market today, premium for dollar remained under pressure due to consistent receiving from exporters.
The benchmark six-month premium payable in May eased to 116-118 paise from 117-119 paise and the far forward October 2018 contract also edged down to 250-252 paise from 252-254 paise previously.
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