The local currency had shed 2 paise to close at 63.44 on Tuesday.
Investors remained cautious in the face of the expiry of November series contracts in the derivatives segment, which also dampened sentiment.
The dollar index eased 0.05 per cent to 98.69.
The rupee fell to an all-time low of 61.21 per dollar, forcing the Reserve Bank of India to intervene to stabilise the currency.
The rupee edged higher by three paise to 66.46 against the US dollar in early trade on Wednesday.
The rupee closed marginally stronger against the dollar on Wednesday.
Rupee closed at 61.86 against the dollar on Tuesday.
The rupee on Monday continued its upward march against the US dollar for the third day, firming up by another 10 paise to 66.00 on fag-end selling of the American currency by banks and exporters.
India Inc is unfazed by the sharp fall of the rupee against the greenback as most big firms have already hedged their foreign exchange exposures.
The company's NetPC works on a 'thin client' concept. This is a small box and does not contain any software or application. It is linked to a central server, which hosts all applications.
The fall comes a day after it hit its highest gain in eight years.
Rupee is likely to remain under pressure due to domestic concerns.
If the greenbacks don't pour in, our markets can't do the Indian rope trick. That has been very evident last week and all of November. The FIIs have just sold stocks worth close to a billion dollars and our markets have taken a 10 per cent or 2,050 point correction.
Most Asian currency and equity markets too suffered steep losses due to US rate hike fears.
The rupee had gained two paise to close at one-month high of 62.14 against the dollar in Tuesday's trade.
Extending losses for the second straight session, the rupee slipped by 11 paise at 66.54 against the US dollar.
India's foreign exchange reserves rose by $2.8 billion to $343.2 billion
The partially convertible rupee closed at 60.30/31 per dollar compared with 60.28/29 on Friday.
The domestic currency has tumbled by 104 paise, or 1.63 per cent, in last six trading days.
Dealers attributed the fall to the dollar's gains after China devalued yuan, which pushed up demand from importers for the US currency.
Weakness in other currencies against the dollar overseas, after US Fed indicating interest rates could rise earlier than expected as the jobs market picking up, also put pressure on the local unit, forex dealers said.
Increased demand for the dollar weighed on the local currency.
The RBI also asked the oil marketing companies to smoothen their daily dollar demand so that upcoming bunched up demand was covered in advance in forward markets or on days with low dollar demand.
The RBI also asked the oil marketing companies to smoothen their daily dollar demand so that upcoming bunched up demand was covered in advance in forward markets or on days with low dollar demand.
If the rupee falls further, it would negatively impact the dollar-based returns of foreign investors, and could influence foreign flows into India.
The domestic currency had last ended at 64.17 per dollar.
There is high demand for the US currency from importers
The rupee had snapped its 3-day losing streak on Thursday.
The rupee recovered from initial losses against the American currency and was quoted higher by 6 paise to 62.00 on fresh selling of dollars by banks and exporters in view of strong foreign capital inflows into equity market.
The 30-share Sensex ended down 90 points at 19,429 after hitting an intra-day low of 19,398 and the 50-share Nifty ended down 40 points at 5,881 after touching an intra-day low of 5,871.
Rupee hits more than two-year low; RBI intervenes
The rupee on Wednesday strengthened by another 3 paise to 62.82 against the US dollar.
The rupee on Friday snapped its two-day gaining streak against the US dollar.
Heavy dollar selling by banks and exporters alongside debt-related inflows largely supported the rupee
The rupee rallied for the second straight session by gaining 21 paise to end at 66.10 against US dollar.
2018 has been a disappointing and highly volatile year for equity investors.
The rupee bounced back by four paise to close at 65.27 per dollar on fresh selling of the American currency by banks.
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