The 30-share index slumped 360.95 points, or 1.02 %, to 35,109.20 in early trade. It had fallen 271.92 points, or 0.76 %, to 35,470.15 in the previous session Monday.
The NSE Nifty too shed 112.30 points, or 1.05 %, to 10,551.20.
The losses on Dalal Street were led by metal, realty, banking, IT, pharma and auto stocks.
Top losers include Yes Bank, TCS, HUL, Kotak Bank, M&M, Sun Pharma, Tata Motors, Infosys, Bajaj Auto, Tata Steel, Reliance, ICICI Bank and SBI, falling up to 3 %.
HDFC was the only gainer on Sensex, trading marginally higher than its previous close.
Financial markets were closed Tuesday on account of Christmas.
According to experts, investors are jittery over the political unpredictability in the US.
US President Donald Trump Tuesday ruled out an end to the partial government shutdown till the Congress approve funds for building a wall along the Mexican border to prevent entry of illegal immigrants.
Democrats and some Republicans have rejected Trump's demand for the US-Mexico border, following which on last week he refused to sign a wider spending bill, temporarily stripping funding from swaths of the government.
Global investors also took cues from Wall Street stocks which plunged for a fourth straight session Monday amid rising doubts over the US economy after Treasury Secretary Steven Mnuchin's efforts to reassure investors fell flat.
Markets were also unnerved by weekend news reports that US President Donald Trump was weighing whether to fire Federal Reserve Chairman Jerome Powell, accounts that Mnuchin said Trump had denied.
The rupee, meanwhile, gained against the US dollar, and was trading at 69.82 a dollar, up 0.46%from its previous close.
Brent crude, the international benchmark, was down 0.43 % at USD 50.55 per barrel.
Stocks of aviation and oil marketing companies rose as crude prices fell. Spicejet and Jet Airways rose up to 2 %, while IOC and BPCL gained up to 1 %.
On a net basis, foreign portfolio investors (FPIs) sold shares worth Rs 577.10 crore Monday, while domestic institutional investors (DIIs) were net buyers to the tune of Rs 186.14 crore, provisional data available with BSE showed.
Elsewhere in Asia, Hong Kong's Hang Seng was fell 0.40 %, Kospi dropped 1.57 % and Shanghai Composite Index shed 0.02 %; while Japan's Nikkei was up 0.65 % in early trade.
On Wall Street, the Dow Jones Industrial Average index cracked 653.17 points, or 2.91 %, to 21,792.20 on Monday.