The 30-share index rose 26.97 points, or 0.10 per cent, to 27,284.61, with sectoral indices led by oil & gas, consumer durables, capital goods, PSU and healthcare trading higher by up to 0.84 per cent.
The initial public offering, which will be open for sale from January 23 to January 25, is likely to value the exchange in a range Rs 4,400-9,000 crore after listing, according to different estimates.
The NSE index Nifty too climbed 18.50 points, or 0.22 per cent, to 8,431.30.
On Monday, the rupee had staged a mild recovery by gaining 6 paise to close at 68.10 on fresh dollar selling by banks and encouraging macro-economic data.
The 30-share Sensex, after shuttling between 27,335.08 and 27,172.68, ended higher by 50.11 points, or 0.18 per cent, at 27,288.17.
Brokers said that the sentiment remained weak in the absence of any positive trigger amid sustained capital outflows by foreign funds.
On Friday, the rupee fell by 8 paise to close at 68.16 against the US currency on fresh bouts of dollar demand from banks and corporates amid capital outflows.
According to brokers, retail inflation easing further to multi-year low of 3.41 per cent in December too had a positive impact.
The gauge had gained 413.86 points in the previous two sessions.
The dollar's weakness against some currencies overseas and early gains in the domestic equity market supported the rupee, dealers said.
The Sensex resumed higher at 26,978.44 and quickly breached the 27,000-mark to hit a high of 27,174.87 before winding up at 27,140.41, scoring a notable rise of 240.85, or 0.90 per cent.
The 30-share index, which gained 173.01 points in the previous session, added 151.01 points, or 0.56 per cent, to 27,050.57 with all the sectoral indices led by metal, capital goods and bank leading the gains.
Meanwhile, the benchmark BSE Sensex recaptured the 27,000-mark by surging 151.01 points, or 0.56 per cent, to 27,050.57 in the opening trade today.
The Sensex opened higher at 26,811.63 and hovered between 26,914.95 and 26,804.17 before closing at 26,899.56, showing a gain of 173.01 or 0.65 per cent
He suggested that in Budget 2017-18, capital gains on sale of gold be abolished if held for more than three years.
Forex dealers said, weakness in the dollar against some other currencies overseas, supported the rupee.
The NSE Nifty rose by 37.50 points or 0.46 per cent to 8,273.55.
The 30-share index, which had lost 119.01 points in the previous session, recovered 23.86 points, or 0.09 per cent, to 26,783.09, with metal, capital goods, FMCG, PSU, banking and oil & gas stocks leading the recovery.
Every day, this exchange at GIFT City will start trading activities at 4 am, when the exchanges in Japan open, and will stop only at 2 am the next day
Through the new international exchange, BSE will look to provide electronic trading platform that will facilitate domestic firms to raise capital in foreign currency by issuing foreign currency dominated bonds.
Shares of Infosys lost 2.50 per cent, TCS went down by 2.18 per cent and Wipro dipped 2.18 per cent on BSE.
The Sensex opened higher and advanced to touch a high of 27,009.61 before ending at 26,759.23, down 119.01 points, or 0.44 per cent.
Sebi Chairman U K Sinha, who was among the financial sector regulators present at the FSDC meeting, offered suggestions for the forthcoming budget for 2017-18.
Zinc prices eased by 0.36 per cent to Rs 177.55 per kg in futures trade on Thursday as speculators reduced their positions, driven by a fall in demand at the spot market.
Oil prices rose in the first trading hours of 2017, buoyed by hopes that a deal between OPEC and non-OPEC members to cut production, which kicked in on Sunday, will be effective in draining the global supply glut.
More than half of the annual gain was on the last trading day.
The Nifty rose 82.20 points, or 1.01 per cent, to end at 8,185.80, after touching the day's high of 8,197.
Forex dealers said weakness of the dollar against other currencies too influenced the rupee uptrend.
The NSE index Nifty was also trading higher by 13.85 points, or 0.17 per cent, at 8,048.70.
Meanwhile, the benchmark BSE Sensex was trading higher by 38.76 points, or 0.15 per cent, to 26,249.44 in early trade.
The benchmark Sensex opened higher and closed at 26,213.44, a gain of 406.34 points, its biggest single-session rally since December 8 when it had gained 457.41 points.
European stocks were trading higher as key indices such as Frankfurt, Paris and London's FTSE rose by up to 0.14 per cent.
Earlier, the Indian rupee opened lower by 10 paise at 67.84 as against Monday's closing of 67.74.
Nifty falls to 7-month low at 7,908.25, down 0.97%
Meanwhile, the stock markets were trading in the red with the benchmark BSE Sensex shedding over 200 points to 25,833.01 points at 1100 hrs.
The NSE Nifty was also trading lower by 79.20 points, or 0.99 per cent, at 7,906.55.