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.
State-owned oil companies gain on continued hopes for a hike in fuel prices: Bharat Petroleum Corp
Still, caution prevails ahead of the Federal Reserve meeting's outcome later in the day.