The Nifty rose 0.54% to 14,563 and the benchmark Sensex rose 0.5% to 49,517.11.
Reliance Industries and HDFC Bank were the top boosts to the Nifty 50, rising 3.2% and 2%, respectively.
Late on Monday, the Financial Stability and Development Council said in a report that the gross non-performing assets of Indian banks might increase from 7.5% in September 2020 to 14.8% under a severe stress scenario.
"When markets are engulfed in this type of (buying) fever these kind of reports do not matter. It is all about liquidity and the fear of missing out," said Umesh Mehta, head of research at Samco Securities, Mumbai.
The Nifty bank index that fell nearly 1% in the morning session, ended up 1.1%, while the Nifty public sector bank index hit a more than 10-month high, surging 6%.
"With COVID-19 vaccination expected soon in India, markets are enjoying a bullish phase and anticipation of a fast recovery is helping the index rise further," said Rahul Sharma, head of research, Equity99 Advisors in Mumbai.
Shares of Gail (India) Ltd rose as much as 5.8% to a 15-month high of 143.5 rupees after the state-owned gas distribution firm said it would consider a proposal to buy back shares.
Tata Motors rose 7.7%, buoyed by a double-digit increase in China sales of its luxury car unit Jaguar Land Rover (JLR).
Indian investors now await retail inflation data due later in the day, with a Reuters poll predicting it fell sharply last month, landing within the Reserve Bank of India's target range.
(Reporting by Nallur Sethuraman in Bengaluru; Editing by Vinay Dwivedi)
By Sethuraman N R