After jumping 272.39 points during the day, the 30-share index turned negative and settled 45.72 points, or 0.13 per cent, down at 34,915.80; while the NSE Nifty slipped 10.30 points, or 0.10 per cent, to 10,302.10.
PowerGrid was the top laggard in the Sensex pack, shedding around 2 per cent, followed by Sun Pharma, ITC, ONGC, Bharti Airtel and Reliance Industries.
On the other hand, Maruti, Nestle India, ICICI Bank and UltraTech Cement were among the gainers.
Indian market pared intra-day gains as participants adopted a wait and watch approach ahead of Modi's address.
Concerns over rising COVID-19 cases and its impact on economic recovery remained a key factor for investors, analysts said.
The number of cases around the world linked to the disease has crossed 1.03 crore and the death toll has topped 5.05 lakh.
In India, the number of infections spiked to 5,66,840 and the death toll rose to 16,893.
Meanwhile, bourses in Shanghai, Hong Kong, Japan and Seoul ended with significant gains.
However, stock exchanges in Europe started on a tepid note.
International oil benchmark Brent crude futures fell 1.36 per cent to USD 41.28 per barrel.
On the currency front, the rupee settled 7 paise higher at 75.51 against the US dollar. ANS MKJ