The Sensex gains 0.26 percent as of 10.37 p.m., after earlier hitting its highest intraday level since February 24.
The Nifty advances 0.19 percent. Both indexes head to their seventh consecutive session of gains.
Some state-owned companies rise on media reports the cabinet will meet on Friday to consider selling some of the government's stake in five companies.
National Aluminium Co Ltd shares gain 4.1 percent, while Hindustan Copper gains 1.7 percent, and Neyveli Lignite Corp rises 3.6 percent.
State-owned oil companies gain on continued hopes for a hike in fuel prices: Bharat Petroleum Corp gains 1.2 percent, while Hindustan Petroleum Corp is up 1.2 percent.
Still, caution prevails ahead of the Federal Reserve meeting's outcome later in the day.