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 4.70 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 spurted up to 2.68 per cent.
During the week, the Sensex declined 544.97 points or 1.72 per cent, while broader Nifty fell 114.65 points or 1.23 per cent.
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.
"Markets settled almost unchanged after hovering in a range, taking a pause after the recent dip. It opened marginally higher but the gains fizzled out in no time and it inched further lower.
"The FM has been announcing the stimulus details for the last two days and hopefully, all the details will be out by Sunday...It seems like markets are awaiting further details before making any reaction," said Ajit Mishra, VP - Research, Religare Broking Ltd.
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.
Announcing the third tranche of the stimulus package post market hours on Friday, she said the measures will focus on giving relief to agriculture and allied industries.
Sectorally, BSE realty, bankex, auto, finance, IT, healthcare and capital goods indices fell up to 1.42 per cent, while telecom, metal, energy, power, oil and gas, basic materials and FMCG rose up to 1.81 per cent.
Broader midcap and smallcap indices fell up to 0.31 per cent.
World equities ticked higher as investors focused on graded resumption of economic activities.
Bourses in Tokyo and Seoul closed with gains, while Shanghai and Hong Kong settled in the red. 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.
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. ANS ABMABM