The BSE Sensex gained over 69 points in early trade on Tuesday on sustained buying by funds and retail investors amid a strengthening rupee.
The buying took place mainly in realty, metal, capital goods, oil and gas and IT sector stocks.
Brokers said sentiments remained firm on sustained buying by participants driven by the Reserve Bank of India's (RBI) plans to inject Rs 8,000 crore into the financial system to ease liquidity and further strengthen the rupee.
Rising for the third straight session, the 30-share index of the Bombay Stock Exchange gained 69.59 points, or 0.33 per cent, to 20,920.33.
In the past two sessions, the Sensex had gone up by 656.34 points.
The 50-share Nifty of the National Stock Exchange traded 18.80 points, or 0.30 per cent, higher at 6,207.80.
In the Asian region, Hong Kong's Hang Seng rose 0.53 per cent while Japan's Nikkei shed 0.73 per cent in early trade on Tuesday.
The US Dow Jones Industrial Average ended 0.09 per cent higher after crossing 16,000 points for the first time in Monday's trade.