Benchmark Nifty50 index was 20 points up at 9,935, while the 30-share Sensex was 85 points up at 32,114 around 9.45 am (IST).
The Sensex of the BSE, which opened at 32,100.22 points, was trading at 32,135.51 points (at 9.18 am), higher 53.62 points or 0.17 per cent from Friday's close at 32,028.89 points.
All the sectoral indices, led by IT, oil & gas, bank and PSU, were trading in the positive zone with gains up to 0.51 percent.
The stock market witnessed a rally in early trade on Monday with both the Sensex and Nifty indices hitting new all-time highs.
According to market observers, investors' sentiments were boosted by hopes of healthy quarterly results from index heavyweights such as Ambuja Cements and HDFC Bank, and buying in consumer durables, banking and FMCG stocks.
Amazon Alexa coming to main Amazon app for Android this week
Also, Alexa on Android can perform different tasks including telling jokes, launching the Netflix app, and ordering Starbucks. The message, which can be read in its entirety below, stated that Alexa was now available through the application.
The broader Nifty surged above 9,950 level to trade at 9,968.05, up by 52.08 points, or 0.53 per cent.
In the Nifty index, Wipro (up 1.68 per cent), Bank of Baroda (up 1.48 per cent), YES Bank (up 1.48 per cent), Reliance Industries (up 1.25 per cent), Hero MotoCorp (up 1.14 per cent) and Bharat Petroleum Corporation (up 0.98 per cent) figured among top gainers.
India VIX closed higher by 2% at 11.3.
However, the rupee depreciated 10 paise, to 64.42 against the dollar in afternoon deals at the forex market.
On BSE, 1,129 stocks were advancing whereas 637 stocks were lagging. Lupin gained 2 per cent followed by Wipro and Reliance Industries.