Equity benchmark Sensex jumped over 150 points to touch its fresh lifetime peak in early trade on Tuesday tracking gains in index majors Infosys, HDFC Bank and Maruti amid persistent foreign fund inflow.

After touching a record intra-day high of 45,582.83, the 30-share BSE index was trading 150.72 points or 0.33 per cent higher at 45,577.69.

Similarly, the broader NSE Nifty rose 44.90 points or 0.34 per cent to 13,400.65. It touched its lifetime intra-day peak of 13,402.70 in early trade.

Maruti was the top gainer in the Sensex pack, rising around 3 per cent, followed by Bajaj Auto, M&M, HCL Tech, UltraTech Cement, HDFC and ONGC.

On the other hand, Tech Mahindra, Sun Pharma, IndusInd Bank, Asian Paints and ICICI Bank were among the laggards.

In the previous session, Sensex soared 347.42 points or 0.77 per cent to its fresh closing peak of 45,426.97, and Nifty rose 97.20 points or 0.73 per cent to an all-time closing high of 13,355.75.

Foreign portfolio investors (FPIs) were net buyers in the capital market as they purchased shares worth Rs 3,792.06 crore on a net basis on Monday, according to provisional exchange data.

"Continued FPI flow remained as dominant factor to drive the market and given consistent weakening to dollar along with increased possibility of new fiscal stimulus, we believe domestic equities will continue to get support from FPIs in the near term," said Binod Modi Head-Strategy at Reliance Securities.

However, irrational exuberance is quite visible in many counters given a sharp rally seen in small cap stocks as investors are pouring money in all stocks irrespective of earnings potential, he said, adding that this could lead to a sizable erosion of wealth especially for retail investors when the cycle turns.

He further stated that US equities closed mostly lower as a continued spike in COVID-19 cases and ambiguity over the quantum of fiscal stimulus led to profit booking.

Additionally, the emerging possibility of no trade agreement deal for Brexit after discussion with European Union leaders and UK officials led to unease about global political development among investors.

Elsewhere in Asia, bourses in Shanghai, Hong Kong, Seoul and Tokyo were trading in the red in mid-session deals.

Meanwhile, the global oil benchmark Brent crude futures were trading 0.82 per cent lower at USD 48.39 per barrel.