According to market experts, participants fear that the Rs 20 lakh crore package may not result in direct and immediate boost to demand, raising doubts over the country's economic revival in the near term.
After slumping over 350 points during the day, the 30-share index pared most losses to settle 25.16 points or 0.08 per cent lower at 31,097.73.
Similarly, NSE Nifty slipped 5.90 points, or 0.06 per cent, to close at 9,136.85.
M&M was the top laggard in the Sensex pack, cracking over 4 per cent, followed by Axis Bank, IndusInd Bank, Hero MotoCorp, Sun Pharma and ICICI Bank.
On the other hand, Bharti Airtel, Asian Paints, Tata Steel, NTPC, HUL and Reliance ended with gains.
Besides uncertainty over the effectiveness of the fiscal stimulus package, the spike in COVID-19 cases in the country is weighing on investor sentiment, experts noted.
Finance Minister Nirmala Sitharaman on Thursday announced a Rs 3.16 lakh crore package comprising free foodgrains for migrant workers, Rs 2 lakh crore concessional credit to farmers and working capital for street vendors in a bid to help those hit hard by the nationwide lockdown.
She is scheduled to announce the third tranche of the government's stimulus package later Friday.
The number of COVID-19 cases in India climbed to 81,970, while the death toll rose to 2,649, according to the health ministry.
Globally, the number of cases linked to the disease has crossed 44.43 lakh and the death toll has topped 3.02 lakh.
Bourses in Shanghai and Hong Kong settled in the red, while Tokyo and Seoul closed with gains.
Stock exchanges in Europe were trading on a positive note in early deals.
International oil benchmark Brent crude futures climbed 2.18 per cent to USD 31.81 per barrel.
On the currency front, the rupee provisionally settled 2 paise lower at 75.58 against the US dollar. ANS ABMABM