The market on Monday witnessed continuous sell-off as the Sensex traded down 9.52 points at 26388.19, and the Nifty down 6.20 points at 8082.40.
With over 1057 shares advancing, Dr Reddy's Labs, SBI, BHEL and Axis Bank were among the top gainers.
On the other hand, TCS, Infosys, Wipro, Maruti and Reliance were down in the Sensex.
The Indian rupee opened lower by 12 paise at 68.08 per dollar on Monday versus 67.96 on Friday.
Pound extended its sell-off near a 31-year low as the fallout from the UK's vote to exit the European Union stoked anxiety among investors around the world.
The market experts expect the rupee to trade with negative bias. Brexit will put more pressure on the rupee.
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Global cues are weak as US market tumbled over three per cent with the Dow losing over 600 points on Friday. Asia markets opened mixed on Monday, as traders continued to digest the UK's unexpected vote.
Brokerage house Deutsche Bank trimmed its Sensex target to 27,000 from 29,000 earlier, citing global uncertainty in the wake of 'Brexit.'
It said that as the long and complicated process of political and economic separation of the UK from the EU unfolds, financial market volatility will remain elevated.
"The risk of markets reacting irrationally will stay elevated," it further added.
The brokerage has advised clients to invest in sectors that have the least exposure to global macro. The only exception is pharmaceuticals as a strong dollar will benefit companies having a sizable exposure to the US market.