Widespread buying was seen in metal, healthcare and realty counters. The equity markets were closed on Tuesday.
Most of the private bank stocks were up in Thursday's trade, keeping the Nifty Private Bank index in the green.
In terms of the broader markets, the S&P BSE mid-cap index inched up by 0.17 per cent and the small-cap index by 0.16 per cent.
The BSE market breadth was, however, bearish as 1,921 stocks declined as against 911 advances.
"Major Asian markets have closed on a positive note, barring the Nikkei and Straits indices".
The management tried to assuage investor concerns a day after the state-owned bank said that it had detected some fraudulent and unauthorised transactions worth about Rs 1.13 trillion ($1,771.69 million) at one of its branches in Mumbai.More news: Donald Trump Jr Criticizes Adam Rippon's 'Olympic Experience Not About Pence' Comment
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U.S. consumer prices rose more than forecast in January as Americans paid more for gasoline, rental accommodation and healthcare, further raising inflation concerns and the prospect of the Federal Reserve hiking interest rates more than initially expected.
Sun Pharmaceutical Industries was marginally lower after its quarterly profit slumped 75 percent.
"If no recovery is possible, the impact could be Rs.42-46 per share out of which the stock price has already fallen - Rs 16 today".
A stronger rupee against the dollar also influenced market sentiment.
DIIs bought shares worth Rs 1,342.70 crore on net basis, while foreign portfolio investors (FPIs) sold shares worth Rs 814.11 crore on net basis on Monday, provisional data showed.