The rupee recovered from more-than three months low of 63.15 in early trade on dollar selling by banks.
It was the second straight week of gains for the benchmarks.
The broader NSE Nifty index too finished lower by 4.80 points, or 0.05 per cent, at 10,632.20.
BSE Sensex on Monday closed nearly 34 points higher at 26,350.17 with gains in realty, power, FMCG and oil & gas stocks amid sustained buying by domestic institutional investors.
Coal India was the biggest gainer on both Sensex and Nifty
The 30-share barometer remained up throughout and hit a high of 29,070.20, powered by a rally in RIL and other blue-chips. The index ended 215.74 points up, or 0.75 per cent, at 29,048.19 -- its highest closing since March 5, 2015, when it had closed at 29,448.95.
The broader Nifty ended on top of 9,800 again.
'The expectation was that Modi would become even bolder in his approach, and after only four months into his second term, we are starting to see evidence of this.'
The rupee extended gains for the fourth straight day against the US currency on Thursday.
SBI had a bad day, sliding the most by 5.36%. Others that dragged the key indices down were M&M, Reliance Industries and L&T.
Sentiment was hurt after market regulator Sebi directed bourses to initiate action against 331 suspected shell companies.
Investors booked profits in recent gainers
The 30-share barometer started higher, but lost its way soon after the railway budget.
In forward market today, premium for dollar declined on sustained receivings from exporters.
Rupee rebounds from one-week low, up 9 paise against dollar.
Investors are keenly focused on new govt's first full-year Budget.
Institutional investors led by foreign portfolio investors have bought these shares.
Sentiment was largely positive after April IIP grew at 4.9 per cent, spurred by higher growth in manufacturing and mining sectors.
Market breadth on the BSE ended firm as 1,908 shares advanced and 1,156 shares declined
The rupee's strength against its competitor could come to haunt exporters.
The broader NSE Nifty too dived by 101.65 points, or 0.97 per cent, to close at 10,350.15.
Coal India topped the losers' list in the Sensex pack on Tuesday, falling 2.36 per cent, followed by Bharti Airtel at 2.16 per cent.
Construction major L&T was the biggest gainer among the Sensex components, spurting 2.30 per cent, after the company said its board has approved a Rs 9,000-crore share buyback plan.
Dealers attributed the rupee's fall to fresh demand for the US currency from importers
Investors have kept their eyes on US-China trade talks and are optimistic about a positive outcome.
On the sectoral map, consumer durables stayed in the lead by surging 2.39 per cent, followed by realty index, oil and gas and infra.
Despite a strong start to trade today, key benchmark indices retreated sharply from their higher levels following bouts of profit-taking amid fresh weakness in the rupee against the dollar.
The 50-share NSE Nifty ended up 37.05 points, or 0.36 per cent, at 10,397.45 points
The Nifty rose 176.50 points, or 1.74 per cent, during the week.
The NSE Nifty settled the day 93.20 points or 0.88 per cent lower at 10,452.30 after shuttling between 10,612.90 and 10,434.05.
Rupee ends day at 61.91 against the US dollar.
But the 30-share Sensex rose by 141.52 points, or 0.41 per cent, to close at 34,297.47. The broader NSE Nifty gained 44.60- points, or 0.42 per cent, to end at 10,545.50 after touching a high of 10,618.10.
The NSE Nifty settled the day 38.85 points or 0.37 per cent lower at 10,500.90 after shuttling between 10,590.55 and 10,456.65, intra-day.
A declining rupee, elevated crude oil prices and sustained foreign fund outflows added to the gloom
'Election years tend to see high government expenditure on unproductive schemes, though that money sloshing around can boost private consumption.' 'Again, it can mean higher inflation,' explains Devangshu Datta.
Muted quarterly earnings, mixed cues from global markets and unabated foreign fund outflows added to the volatility
The dollar maintained its bullish momentum in Asian and early European trade
In the longest losing streak of 2017, the BSE Sensex has lost 1,270 points, or 3.91 per cent. It fell to a three-month low of 31,154.03 on Wednesday.
The 30-share Sensex, after opening on a strong footing, continued its upward march to hit an all-time high of 35,827.70. The NSE Nifty also hit a record intra-day high of 10,975.10, before finishing at 10,966.20, up 71.50 points.
The rupee resumed marginally lower at 67.24 per dollar against Wednesday's closing level of 67.21.
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