The NSE's India VIX, a gauge of the market's expectation of volatility over the near term, jumped 5.70% to 17.33.
The market breadth, indicating the overall health of the market, was strong. On the BSE, 1,922 shares rose and 509 shares fell.
Investors were cautious ahead of the Federal Reserve's decision on interest rates and release of economic forecasts on Wednesday.
Asian stocks traded mixed on Tuesday as investors look ahead to the release of US consumer inflation data for August.
The S&P BSE Sensex, advanced 226.47 points or 0.41% to 55,555.79 on Monday. The Nifty 50 index gained 45.95 points or 0.28% to 16,496.45.
US stock indexes closed lower Friday, with renewed concerns about a rise of cases of the delta variant Covid-19 and disappointing results from Amazon.
In the previous session, the BSE Sensex gained 295 points to close at 49,502, while the Nifty50 rose 119 points to 14,942
As many as 27 stocks in the Sensex pack traded in the green with Power Grid rising the most 3.73%.