Trading along the line of resistance, the domestic currency largely moved in a narrow range throughout the day.
Foreign portfolio investors had sold shares worth a net Rs 168.84 crore on Thursday, as per Sebi data.
A hawkish RBI tone in its latest minutes also dampened sentiment.
Reserve Bank of India (RBI) Governor Urjit Patel told the Monetary Policy Committee (MPC) that there is room for banks to further cut interest rate while sounding a note of caution on inflation front in the coming months.
Domestic bourses failed to maintain their early buoyancy and gave up its gains to end lower following profit taking even as tepid corporate earnings and geopolitical jitters weighed on sentiment.
It lost further ground to hit an intra-day low of 64.67 before rebounding sharply to trade briefly higher at 64.55 mid-morning deals.
Having failed to build on early upmove, the domestic unit once again turned shaky towards the fag-end trade to settle lower at 64.61, showing a loss of 5 paise, or 0.08 per cent.
It had gained 7 paise in last two days.
The RBI, meanwhile, fixed the reference rate for the dollar at 64.5701 and for the euro at 69.1675.
In worldwide trade, the greenback shook off early weakness to trade little changed against a basket of major currencies as the latest data on domestic jobless claims and business activity in the mid-Atlantic region did not change traders' views of modest US economic growth and low inflation.
In cross-currency trade, the Indian unit advanced further against the pound sterling to end at 82.55 from 82.57 per pound and recovered against the euro to finish at 69.16 compared to 69.37 earlier.
The home unit reiterated against the Japanese Yen to close at 59.23 per 100 yens from 59.19 yesterday.
On the equity front, the flagship Sensex declined over 57 points to end at 29,365.30, while broader Nifty moved down 17 points to 9,119.40.
In the forward market today, the premium for dollar recovered due to fresh paying pressure from corporates.
The benchmark six-month premium for September edged higher to 144-146 paise from 142-144 paise and the far-forward March 2018 also moved up to 303.5-305.5 paise to 299-301 paise on Thursday.
In the global commodity front, crude prices fell back sharply to mark its biggest weekly drop in a month on doubts that an OPEC-led production cut will restore balance to an oversupplied market.
The global benchmark Brent crude futures were trading at $52.87 a barrel in early trade.