The benchmark BSE index closed up 0.31 percent at 36,582.74 while the broader NSE index ended 0.17 percent higher at 10,912.25.
Both the indexes gained for the third straight session.
Shares of Reliance Industries closed up 3.16 percent while those of HDFC edged 0.7 percent higher.
Reliance Communications Ltd (RCom) shares plunged by more than half to a record low on Monday, after the Indian telco said it will seek a fast-track resolution to its indebtedness through bankruptcy court.
In one of India's most high-profile bankruptcy filing cases, RCom said lack of regulatory approval for asset sales as well as cases pending at the Supreme Court and Telecom Disputes Settlement and Appellate Tribunal (TDSAT) resulted in its decision to approach the National Company Law Tribunal (NCLT).
The Mumbai-based telco also said its lenders had not received any proceeds from asset monetisation plans, and that its overall debt resolution process had not made any progress.
Competition in India's telecoms industry has stepped up several levels since the 2016 entry of cut-price player Reliance Jio Infocomm Ltd, leading to RCom shutting down its wireless communications business. Reliance Jio is owned by Mukesh Ambani, the elder brother of RCom owner Anil Ambani.