Reuters Market Eye - The BSE Sensex is higher 0.3 percent and the broader Nifty is up 0.4 percent, after hitting their highest intraday level since January 24.
IDFC Ltd is up 2.7 percent on hopes of getting a bank licence, dealers say.
An advisory committee is due to give its recommendations on bank licences by this weekend to the Reserve Bank of India, the Business Standard newspaper reported on Tuesday citing India's Financial Services Secretary, Rajiv Takru.
Ambuja Cements Ltd shares gain 2.6 percent on continued hopes of a price hike.
Overseas investors bought Indian shares worth 2.67 billion rupees on Monday, provisional exchange data shows.
Foreign investors have been net buyers of nearly $450 million over the last nine sessions, helping ease some of the concerns in a year dominated by worries about the U.S. Federal Reserve's tapering of its monthly bond buying and the outlook for China's economy.
(Reporting by Abhishek Vishnoi)