The NSE Nifty 50 index closed up 0.2% at 11,896.8, while the S&P BSE Sensex ended 0.28% higher at 40,544.37.
India's Prime Minister Narendra Modi is set to address the country at 1230 GMT on Tuesday.
India posted its lowest daily coronavirus caseload in nearly three months, data from the health ministry showed on Tuesday, as new cases maintained a decreasing trend from a peak in September.
Shares in HDFC Bank Ltd rose as much as 2% after ratings agency S&P said the lender's asset quality over the next two years would remain superior to the industry despite likely deterioration from the pandemic.
The Nifty Bank Index, which slipped as much as 0.9% earlier in the day, ended the session 0.19% higher and extended gains for a third straight day.
IT stocks were among the top gainers on the Nifty 50, led by gains in HCL Technologies Ltd and Tech Mahindra Ltd , which rose 4.1% and 3.1%, respectively. The Nifty IT Index ended 1.4% higher.
Hindustan Unilever Ltd ended the day 0.2% lower after the consumer giant reported a quarterly profit that missed estimates.
Oberoi Realty rose as much as 20% to its highest since March after J.P.Morgan raised its price target and earnings estimate for the firm, helping the Nifty Realty Index end 3.9% higher.
(Reporting by Philip George in Bengaluru; Editing by Ramakrishnan M.)