At the Interbank Foreign Exchange market, the domestic unit commenced higher at 61.80 a dollar from previous close of 61.92.
The rupee on Tuesday gained 14 paise to close at 61.88 against the dollar.
The fall came on the back of a massive selloff in NBFCs, led by DHFL which skidded over 50 per cent on fears of a liquidity crisis.
The broader NSE Nifty scaled a high of 10,856.55 before closing up by 55.90 points, or 0.52 per cent
Retail inflation rose 4.38 per cent year-on-year in November, the slowest pace in data going back to January 2012.
The rupee had lost 21 paise on Tuesday's trade.
HDFC Bank was the top loser in the Sensex pack, falling 2.99 per cent, followed by Adani Ports at 2.87 per cent.
Stock markets in structural bull run but there can be bouts of volatility says Ravi Gopalakrishnan, head, equities, Canara Robeco Mutual Fund
Rupee is seen strengthening against the dollar.
A widening probe by US authorities involving top drug companies following complaints of price fixing of generics was a point of worry for the participants, said analysts.
The BSE Sensex jumped 70.42 points to end at 34,503.49, while the broader NSE Nifty finished at 10,651.20, up 19 points.
Sensex has shed over 150 points in afternoon trade.
Other than ITC, other laggards include PowerGrid, Infosys, M&M, NTPC, SBI, HDFC, Kotak Bank, HDFC Bank, TCS, Hero MotoCorp, Coal India, ONGC, RIL, Asian Paint, IndusInd Bank, ICICI Bank, Maruti Suzuki, Bajaj Auto, Tata Motors, Bharti Airtel and Axis Bank.
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 NSE 50-share Nifty also closed higher by 61.60 points, or 0.59 per cent, at 10,504.80 after shuttling between 10,513 and 10,441.45.
Yes Bank was the top gainer in the Sensex pack, surging 3.76 per cent, followed by SBI at 3.18 per cent.
The ongoing corporate results and the Union budget are also making participants tread cautiously though the GST agreement provided some relief.
It, however, was a record-smashing week for both the indices, which scaled their lifetime highs.
Sustained demand for the dollar is the reason.
The rupee on Wednesday strengthened by another 3 paise to 62.82 against the US dollar.
Market participants attributed the robust inflows to positive investor sentiment
Sustained FII inflows and fresh spell of buying by domestic institutional investors fuelled the rally
The restraint on part of investors was chiefly because of RBI's minutes of its December policy meeting, which showed that some members were concerned about rising oil prices, its inflationary impact and possibility of fiscal slippage.
Analysts expect the inflows to accelerate further.
It was an extremely volatile session, borne out by the Sensex swinging over 1,200 points through the day and the Nifty 369 points.
Profit-booking by participants in view of the domestic markets' recent record-setting run fuelled the downtrend
The broader NSE Nifty closed 1.25 points, or 0.01 per cent down at 10,564.05.
The 50-issue NSE Nifty in range-bound movements settled higher by 59.15 points, or 0.58 per cent, at 10,252.10.
Geo-political concerns over death of a Saudi journalist, Brexit and likely breach in Italy's budget also kept investors cautious.
Covering-up of pending short positions on expiry of the July derivatives contracts and a strengthening rupee propped up the markets at high levels
The Nifty finished the day at 10,265.65, a hefty gain of 98.95 points, or 0.97 per cent, after shuttling between 10,270.85 and 10,195.25.
The rupee snapped 2-day rise to end weaker against the dollar on Thursday.
The wider Nifty hit a low of 10,033.35 before finishing at 10,044.10, down 74.15 points or 0.73 per cent.
The Indian benchmark S&P BSE Sensex today eased by 14.59 points, or 0.05 per cent after touching its all-time intra-day peak.
Small- and mid-cap stocks continued facing selling pressure due to stretched valuations.
Rupee falls 5 paise against dollar, ends at 61.92.
A weak dollar in overseas market boosted the rupee sentiment
Sun Pharma was the biggest gainer in the Sensex pack, advancing 1.79 per cent.
Bank stocks rose sharply by up to 12 per cent after the government's move to withdraw 500 and 1,000 rupee notes from circulation as part of black money crack down
The wider NSE Nifty touched a low of 10,652.40 before finishing at 10,671.40, showing a loss of 97.75 points, or 0.91 per cent.
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