Sources said the decision was taken at a meeting of the Standing Committee on Finance, headed by Congress' M. Veerappa Moily.
Last month, Patel said the RBI's regulatory powers over PSBs were weaker than those over the private sector banks.
According to the sources, the parliamentary panel would ask the RBI Governor questions about the frauds and better regulation.
Sources said some members also referred to reports of cash crunch in different parts of the country.
Finance Ministry officials answered some queries and sought three weeks to file replies to the others.
Sources said Insolvency and Bankruptcy Board of India Chairman M.S. Sahoo was also present.
Sources said BJP member Nishikant Dubey said that RBI had failed to discharge its role in preventing bank frauds and has sought changes in the Reserve Bank of India Act 1934 to fix responsibility in such cases.
Sources said some opposition members asked if middle-level officials were the only ones responsible for the PNB fraud and if it was a systemic failure. They said in the frauds surfacing in the banking sector, there were mistakes which were being repeated.
A member asked about the pace of corrective measures implemented in the wake of the frauds and what more needs to be done.
The panel members also raised queries about the controversy over conflict of interest in the Rs 3,250 crore loan given by the ICICI Bank to the Videocon Group in 2012. The controlling shareholder of Videocon Group co-founded a separate company with the spouse of ICICI's CEO Chanda Kochhar. A significant portion of the loan has since become non-performing.
Another source said the panel discussed the situation in the banking sector and the way ahead with questions about the non-performing assets, Insolvency and Bankruptcy Code and auditing standards.
"It was more of a questioning meeting," the source said.
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