Data showing foreign institutional investors have slowed their purchases in domestic shares further added to the weak sentiment.
India is seen as being particularly vulnerable to foreign selling because of its current account deficit.
Traders also worry the rupee could be hit as a large part of the dollar demand by state-run oil companies, which was diverted to a special window by the Reserve Bank of India in August, has returned to markets recently.
"FII (foreign institutional investor) inflow fatigue is high given the year-end, weighing on INR," said Suresh Kumar Ramanathan, head of regional interest rate and FX strategy at CIMB Investment Bank, Kuala Lampur.
Ramanathan expects rupee to hit 62/dlr by year end, but any risk of a tapering could push it towards 65.00.
The partially convertible rupee closed at 62.93/94 per dollar, compared to 62.57/58 on Wednesday. It weakened as much as 63 during the day, its lowest since November 14.
The Reserve Bank of India was spotted selling dollars early in the session, according to two traders.
Some dealers also cited intervention on Wednesday, although there was no consensus.
Fed tapering concerns were sparked after minutes from its October meeting released on Wednesday signalled the central bank could start scaling back the asset purchases at one of their next few meetings provided this was warranted by economic growth.
The previous spell of Fed tapering fears had sent the rupee to a record low of 68.85 in late August.
Traders also cited regulatory and exchange data showing foreign institutional investors bought shares worth 800 million rupees on Wednesday, compared with more than 10 billion rupees each on Monday and Tuesday.
In the offshore non-deliverable forwards, the one-month contract was at 63.43, while the three-month was at 64.53.
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