The domestic unit closed higher by 11 paise at 66.56 in Wednesday's trade.
Weakness in euro against the dollar weighed on the rupee.
The rupee on Monday gained for the first time in three days and closed up 12 paise to 62.56 against the dollar on fag-end sales of the US currency.
The domestic unit hovered in a range of 66.45 and 66.61 per dollar during the day.
Nifty futures traded in Singapore were trading down 0.8 percent in line with other emerging Asian markets.
The rupee had dropped 18 paise against the dollar on Thursday.
Weak domestic shares and foreign institutional investors' selling about 39 billion rupees of index futures in the last four trading sessions weighed on the rupee, dealers said.
At the Interbank Foreign Exchange market, the domestic currency commenced weak at 55.68 a dollar from Monday's close of 55.57 against the dollar.
The domestic unit had lost 7 paise to close at 66.87 in Tuesday's trade.
The Bombay Stock Exchange, the National Stock Exchange, the interbank foreign exchange market and overnight call money/government securities market will remain closed on Wednesday.
However, the US dollar's strength against other currencies overseas capped the rupee's gain
The rupee had closed barely steady at 63.75 on Wednesday.
Cautious optimism over US-China trade talks after US President Trump said his trade negotiators had received two "very good calls" from Beijing also influenced the local currency, dealers said.
SBI managing director PK Gupta told reporters that the rupee has been faring better than many of its peers, including the Turkish, Argentinean, and Indonesian currencies.
The rupee lost 37 paise to end at 62.60 against the dollar on Tuesday following demand for the US currency and a fall in local equities on further rate hike concerns.
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In global markets, the dollar declined against key rivals in early trade as investors weighed the prospects for a continuation of monetary stimulus from the US Federal Reserve.
Increased selling of the US dollar by exporters supported the rupee.
The rupee has lost 23 paise or 0.35 per cent in two days.
The fall would have been much more pronounced, had there not been sustained capital inflows worth of over $100 million in equities, forex dealers said.
The rupee ended lower by six paise at 65.73 against the US dollar on Monday.
Despite a heavy battering, the rupee on Tuesday made a smart recovery to close at 63.25 after hitting a fresh low of 64.13 against the US dollar, helped by RBI's massive intervention.
In New York, the dollar fell against other major currencies on Monday after a December reading on the US services sector came in below market expectations.
The dollar index, a gauge of six major currencies, was down by 0.13 per cent as it lost ground against the euro following a better-than-expected survey of German sentiment.
A lower opening of the domestic equity market put pressure on the rupee.
The rupee on Wednesday dropped by 73 paise to 61.20 in the late morning deals on persistent month-end dollar demand from importers on the back of strengthening in the US currency overseas.
Investors are anxious over the US-China trade tension, a sharp devaluation in yuan and uncertainty over Kashmir issue.
The local currency had gained five paise to close at 66.35 in Monday's trade.
The US dollar bought 99.40 yen in Asian trade, compared with 99.21 in North American trade late on Monday.
This is the first time since June 27 that the domestic currency has fallen below the 60 level.
Finance Minister P Chidambaram in an interview to PTI on Monday said, 'sentiment will turn in favour' of the rupee as government is 'committed to containing the fiscal deficit' within target and is addressing how to finance CAD.
Forex dealers said besides dollar weakening against the euro in overseas markets, higher opening in the equity market and increased foreign funds inflows mainly supported the rupee.
Fresh dollar selling by exporters on hopes of fall in the USD after downward revision to that country's first quarter GDP growth also helped rupee recover as hopes surfaced that the Fed may delay the plan to taper of monetary stimulus.
Forex dealers said besides dollar gaining against other currencies in the global markets, a lower opening in the domestic equity market also, influenced the rupee.
The industrial production grew by two per cent in September, mainly on account of better performance by power and mining sectors.
Besides, dollar's weakness against some Asian currencies supported the local unit, forex dealers said.
The local currency had surged 35 paise to 63.65 in Thursday's trade.
The dollar index was down by around 0.15 per cent against a basket of six major global currencies.
The rupee is seen weakening against dollar in current week.
The rupee on Monday appreciated by 11 paise to 54.64 against the US dollar in early trade at the Interbank Foreign Exchange, aided by selling of the American currency by exporters and banks.
However, foreign capital inflows into equity market restricted the rupee's fall to some extent.
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