Shares of IT, technology, banking, capital goods, consumer durables and realty sectors rose on good buying enquiries.
The Sensex resumed higher at 19,689.09 and shot up further to a high of 19,830.56 before quoting at 19,826.72 at 1030hrs, showing a net gain of 163.08 points, or 0.83 per cent from its last weekend's close.
The NSE 50-share Nifty also firmed up by 42.70 points or 0.72 per cent to 5,994.00 at 1030hrs.
Major gainers were Infosys (3.89 per cent), TCS (2.31 per cent), ICICI Bank (1.65 per cent), ONGC (1.44 per cent) and Wipro (1.17 per cent).
Foreign institutional investors (FIIs) bought shares worth a net Rs 825.18 crores on last Friday as per provisional data from the stock exchanges.
Most Asian stocks rose in the early trade. Key benchmark indices in China, Hong Kong, Indonesia and South Korea rose by 0.25 per cent to 2.06 per cent while indices in Singapore and Taiwan fell by 0.4 per cent to 0.58 per cent.