Overall forex market sentiment remained largely dull in the absence of any major triggers even as currency traders preferred to stay on the sidelines and avoided taking any long positions ahead of Christmas holiday.
Heavy sell-offs by foreign investors and funds largely weighed on the forex trading.
Foreign portfolio investors (FPIs) pulled out worth Rs 1,505.04 crore from the equity markets yesterday.
The Indian unit traded in a narrow range of 64.00-64.13 most of the day before settling positively.
Meanwhile, domestic bourses hit a soft patch for the second day running on the back of profit-taking in select front-line counters amid bearish global sentiment.
Most Asian markets slipped as investors took some cash out despite the passage of long-awaited US tax legislation through Congress.
The flagship Sensex shed over 21 points to end at 33,756.28, while Nifty slipped 4 points at 10,440.30.
But, it soon fell back to trade in negative terrain due to stray dollar demand from some foreign banks.
After a brief slippage, the home currency rebounded in mid-afternoon trade and finally settled at 64.06, showing a gains of 0.05 paise, or 0.08 per cent.
It had lost 11 paise yesterday against the USD.
The RBI, meanwhile, fixed the reference rate for the dollar at 64.0883 and for the euro at 76.0344.
In cross-currency trades, the rupee recovered against the pound sterling to close at 85.65 from 85.89 per pound and also bounced back against the Japanese yen to finish at 56.43 per 100 yens from 56.68 yesterday.
The local currency, however, drifted further against the euro to end at 76.05 from 75.94 earlier.
Elsewhere, the common currency euro and pound sterling traded lacklustre against the US Dollar after the US House of Representatives approved final version of tax bill.
The benchmark six-month premium payable in May moved down to 121-123 paise from 122-124 paise and the far forward October 2018 contract also declined to 255-257 paise from 259-261 paise previously.
On the global energy front, crude prices fell back after the operator of Britain's Forties pipeline in the North Sea said it was expected to restart in early January after repairs over Christmas.
Oil prices have risen since the pipeline was shut on December 11.
The benchmark Brent is trading 23 cents down at USD 64.33 per barrel in early Asian trade.
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