The 30-share barometer, which had lost 156.85 points yesterday, fell further by 84.18 points, or 0.53 per cent, to 15,942.23 in early trade, with banking, consumer durable and FMCG sectors stocks led the fall.
Similarly, the wide-based National Stock Exchange index Nifty declined by 23.10 points, or 0.48 per cent, to 4,837.40.
Brokers said depreciating rupee, which plunged to a record low of 55.39 against the US dollar yesterday, raised concerns of slowing economic growth.
They said a weak trend on other Asian markets following overnight losses at the US market, also influenced the trading sentiment here.
In the Asian region, Japan's Nikkei fell by 1.21 per cent, while Hong Kong's Hang Seng shed 1.54 per cent in early trade. The US Dow Jones Industrial Average ended marginally 0.01 per cent lower in yesterday's trade.