The S&P BSE Sensex index rose as much as 102.09 points to touch 40,447.17 on the upside amid choppy trade, and the broader NSE Nifty benchmark climbed to as high as 11,946.80, up 33.35 points from the previous close.
Equities in other Asian markets as well as Wall Street futures fell amid growing worries that US-China trade talks are stalling.
MSCI's broadest index of Asia-Pacific shares outside Japan fell 1.01 per cent to the lowest in more than a week. Hong Kong shares slumped 1.8 per cent to a two-week low, battered by fears that anti-government protests appear to be spiralling out of control.
Sensex had on Monday ended 21.47 points - or 0.05 per cent - higher at 40,345.08 and the Nifty settled at 11,913.45, up 5.30 points from the previous close, after a volatile session. The share markets remained shut on Tuesday.