The benchmark BSE index closed the session 0.36 percent higher at 35,980.93, while the broader NSE index ended up 0.28 percent at 10,802.15.
Gains on the NSE index were driven by ICICI Bank Ltd, with shares rising 3.4 percent to a record high close.
Shares of Bandhan Bank Ltd fell to their lowest since December, while Gruh Finance Ltd tumbled as much as 17.41 percent to their lowest since October.