The rupee is expected to fall further to 69.50 by year-end.
The NSE index Nifty also recaptured the 8,300 level by inching up 30.05 points, or 0.36 percent, to 8,303.85.
Ahead of the budget, regulator Sebi on Thursday said equity markets are well regulated and it has made certain suggestions for deepening of capital markets.
The Sensex rebounded strongly to end near a two-month high of 26,878 by zooming over 245 points and the NSE Nifty rescaled the 8,200-mark after the US Fed minutes hinted at the uncertainty over the pace of rate hike.
The 30-share index was trading higher by 171.39 points, or 0.64 percent, at 26,804.52 with all sectoral indices led by metal, auto, realty and banking stocks in the green.
The rupee made a roaring comeback after a two-day downfall against the American currency and ended higher by 28 paise at 68.05 Wednesday following a fresh bout of dollar selling by banks and exporters.
The benchmark BSE Sensex advanced over 58 points in early session today on continuous buying by domestic institutional investors amid strong global leads.
Mutual Fund industry has added more than Rs 3.5 lakh crore to its asset base in 2016 to reach Rs 17 lakh crore mark, primarily on account of growing interest from retail investors and aggressive buying of stocks.
The BSE Sensex made a modest recovery of over 43 points at the start on Tuesday on fresh buying, buoyed by a pick-up in infrastructure sector in November coupled with firm Asian cues.
The Cabinet Committee on Parliamentary Affairs (CCPA) will meet on Tuesday to take a call on advancing the Budget Session of Parliament to the last week of January.
Opening on a weak note, the Sensex shuttled between 26,720.98 and 26,447.06 and settled lower 31.01 points, or 0.12 percent, at 26,595.45.
The rupee started 2017 on a weaker note and plummeted by a whopping 30 paise to 68.22 against the US dollar due to huge demand for the American currency.
BSE's India International Exchange at GIFT city will go live for trading post the festival of 'Makar Sankranti' later this month, and will offer only derivative products for the first six months at least.
Stock markets opened on a subdued note on the first trading day of 2017, with the benchmark BSE Sensex falling over 132 points in early trade on profit-booking after recent gains.
Stock market trends this week will largely depend on domestic as well as global macro economic data prints, while expectation of tax sops in budget and weakness of dollar may add to the positive sentiment for the year ahead, experts say.
Muthoot Finance has raised its stake further in subsidiary firm Belstar Investment and Finance Pvt Ltd (BIFPL) to 64.60 per cent.
Snapping the last 2-week losing streak, BSE benchmark Sensex and CNX Nifty regained by 586 points and 200 points respectively on bargain hunting from domestic mutual funds despite selling from foreign funds.
India's stock market rises for second straight day on the final trading session of 2016, Friday amid further strength in the rupee.
In a bid to further develop India's debt markets, the Reserve Bank on Thursday said trading of interest rate options will be permitted from January 31, 2017.