Mumbai benchmark indices rebounded after falling in early trade on Thursday, with the Sensex breaching the historic 79,000 mark for the first time and the Nifty hitting its new record high, amid buying in blue-chip stocks.

The 30-share BSE Sensex jumped 339.51 points to hit its new all-time high of 79,013.76 after falling in early trade, helped by buying in blue-chip companies such as Reliance Industries and ICICI Bank.

The Nifty also recovered, rising 97.6 points to hit its new all-time high of 23,966.40.

Among the 30 Sensex companies, UltraTech Cement, JSW Steel, Reliance Industries, Axis Bank, ICICI Bank, Bajaj Finance, Kotak Mahindra Bank and Tata Steel gained the most.

Maruti, Tech Mahindra, HCL Technologies and Larsen & Toubro were the biggest laggards.

“The market will remain bullish in the near term despite valuation concerns, and the current momentum has the potential to take the Sensex to 80,000 levels.

"A healthy trend in the market is that the bullish movement is now led by fundamentally strong large-cap companies in sectors such as banking and telecom. With RIL, which had not participated in the rally until yesterday, joining the bullish bandwagon, the rally has the strength to continue," said VK Vijayakumar, chief investment strategist at Geojit Financial Services.

In Asian markets, Seoul, Tokyo, Shanghai and Hong Kong traded lower.

US markets ended in positive territory on Wednesday.

Foreign institutional investors (FIIs) offloaded shares worth Rs 3,535.43 crore on Wednesday, according to exchange data.

Global benchmark Brent crude fell 0.21 percent to $85.07 a barrel.

BSE benchmark Sensex rose 620.73 points or 0.80 per cent to settle at a fresh closing high of 78,674.25 on Wednesday.

The Nifty rose 147.50 points or 0.62 per cent to settle at a record closing peak of 23,868.80.