Around 3.30 p.m., the wider Nifty of the National Stock Exchange (NSE) provisionally closed at a new high of 9,891.70 points -- up by 75.60 points, or 0.77 per cent.
It recorded a new intra-day high of 9,897.25 points.
The 30-scrip Sensitive Index (Sensex) of the BSE breached the 32,000 points-mark for the first time and touched a record high of 32,091.52 points during intra-day trading on Thursday.
The Sensex, which opened at 31,896.23 points, closed at 32,037.38 points -- up 232.56 points, or 0.73 per cent, from its previous close at 31,804.82 points.
The Sensex recorded a low of 31,892.63 points during the intra-day trade.
"Global equities traded higher after US Federal Reserve Chair Janet Yellen, hinted at more gradual tapering programme at her testimony before the US Congress," said Dhruv Desai, Director and Chief Operating Officer of Tradebulls.
"India's retail inflation hit a record low of 1.54 per cent in June, lowest since 1999, raising hopes of an interest rate cut by RBI (Reserve Bank of India) ahead of monetary policy next month (in August)."
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