MUMBAI: Equity benchmark indices Sensex and Nifty on Tuesday hit fresh lifetime highs before closing flat led by profit-booking in select banking and telecom stocks amid concerns over rich valuations.

In volatile trade, the 30-share BSE Sensex closed at 79,441.45, down 34.74 points or 0.04 per cent. During the day it jumped 379.68 points or 0.47 percent to hit a record high of 79,855.87.

Nifty fell by 18.10 points or 0.07 percent to 24,123.85. It rose 94.4 points or 0.39 per cent to an intra-day high of 24,236.35.

Kotak Mahindra Bank, Bharti Airtel, IndusInd Bank, Tata Motors, ICICI Bank, Bajaj Finance, State Bank of India and Titan were the biggest laggards in the Sensex pack.

Larsen & Toubro, Infosys, HDFC Bank, Tata Consultancy Services, HCL Technologies and Tata Steel were the top gainers.

On Monday, the BSE benchmark closed at an all-time high of 79,476.19, up 443.46 points or 0.56 per cent. Nifty closed at a new high of 24,141.95, up 131.35 points or 0.55 per cent.

In Asian markets, Tokyo, Shanghai and Hong Kong closed in positive territory on Tuesday, while Seoul closed lower.

European markets were trading with losses. On Monday, American markets closed in the green.

India's gross GST collections rose 8 per cent to Rs 1.74 lakh crore in June, sources said on Monday.

Global oil benchmark Brent crude rose 0.66 percent to US$87.17 per barrel.

According to exchange data, foreign institutional investors (FIIs) sold equities worth Rs 426.03 crore on Monday.