Brokers said stocks also got support from the RBI's assurances that the central bank would take measures to provide adequate liquidity in the banking system.
The 30-share Sensex, which had gained 63 points in the previous session, added 37.61 points, or 0.19 per cent to 19,893.85, after moving between 19,997.28 and 19,826.99.
The 50-scrip National Stock Exchange index Nifty advanced 8.40 points, or 0.14 per cent to 5,882.25. It shuttled between 5,917.65 and 5,864.10 during the session.
"Being the expiry day for the derivatives segment, more volatility was expected. It seems that the markets have calmed down and stabilised after the heavy volatility we witnessed last week. The rupee also stayed range-bound, appreciating slightly to the 62 mark," said Raghu Kumar, co-founder of brokerage firm RKSV.
A firming Asian trend and lower opening in Europe ahead of U.S. Jobless claims, also influenced the trading sentiment in domestic markets to some extent, traders said.
In Sensex, the major support came from Sun Pharma that surged to an all-time high of Rs 586.80 and closed at Rs 583.50 on hopes of higher sales of a key cancer drug following reports the drug would likely to be in short supply soon.
Overall, 15 stocks in Sensex climbed while 15 other declined. Sectorally, the BSE Healthcare sector index gained the most by rising 0.83 per cent, followed by Power index by 0.82 per cent. Bucking the trend, the stocks of oil and gas, consumer durables, realty, IT sectors ended with losses.