In a letter to the Reserve Bank of India (RBI), the government said the failure to detect the fraud, the biggest ever in India's banking sector, raised questions about the central bank's "efficacy of supervision to detect and check systemic failure", NewsRise and other media reported.
"Either the framework designed by RBI to prevent and detect such frauds is inadequate or RBI is unable to ensure its effective implementation," they quoted the letter as saying.
The RBI did not immediately respond to a request for comment today, which was a holiday in Mumbai. A finance ministry spokesman declined comment.
Rajeev Kumar, the top government official overseeing banks, told Reuters in New Delhi the Finance Ministry had written to banks to take effective steps to avoid a repeat of a PNB-like fraud. Mr Kumar declined to comment if the government had written to the RBI.
But in among the first official response by the Finance Ministry, he said the Punjab National Bank will need to honour the "bonafide" transactions that have occurred through the bank's platform.
The government action comes as police briefly locked down the PNB branch in south Mumbai that was at the heart of the scam and continued searches today to gather evidence. The bank would have been closed on Monday anyway because of the holiday.
A source at the Central Bureau of Investigation (CBI) said the branch was likely to resume operations tomorrow.
Besides searching the premises, the police also questioned more PNB officials today, the CBI source said, taking the total number of bank staff who have been questioned so far to 13.
Three people, including two employees of PNB, India's second largest state-run lender, were arrested and presented before a Mumbai court over the weekend in the case that involves billionaire jeweller Nirav Modi.
Police also questioned some executives from Nirav Modi's group, the source said.
The bank has said that the two employees arrested by police colluded with companies belonging to Modi and another jeweller Mehul Choksi, who heads jewellery retailer Gitanjali Gems Limited and other companies.
Jeweller Modi, whose clients include Hollywood stars such as Kate Winslet and Dakota Johnson, has not commented on the allegations. Police have said Modi and his family left India before PNB filed a complaint on the alleged fraud.
Mr Choksi has also not commented, and police have said he also left India last month.
PNB shares plunge
PNB has said the two bank officials issued fraudulent letters of undertaking to overseas branches of other Indian banks which lent money to the jewellers based on the guarantee from PNB.
All the letters of undertaking were issued by the two employees who were working at the Brady Road branch in south Mumbai.
PNB shares slid for a fourth straight day today, closing 7.2 per cent lower. The sell off has wiped out about Rs 10,000 crore, or more than a quarter of the bank's market value, since it disclosed the fraud last Wednesday.
Meanwhile, in a sign of the widening fallout from the PNB case, shares of Choksi's Mr Gitanjali Gems fell 9.9 per cent after its chief financial officer and company secretary resigned today.
In a letter shared with stock exchanges, Company Secretary Pankhuri Warange said she was resigning because of the company's lack of disclosure despite her advice to be forthcoming.
"I have advised the management on the required disclosures to be made. There is, however, no consensus in my opinion on the disclosures to be made and that of the management, and in these circumstances, my conscience doesn't permit me to continue with my position," she wrote.
Ms Warange did not disclose additional details.
The other executive, Chief Financial Officer Chandrakant Karkare, cited his wife's health as the reason for his resignation, according to a Gitanjali filing to stock exchanges.
A representative for Gitanjali, which last week denied Choksi's involvement in the alleged fraud, did not respond to requests for comment today.
Other bank stocks with exposure to the fraudulent transactions that PNB says began in 2011 also fell.
UCO Bank, another state-run lender that has said it had nearly Rs 2,600 crore in exposure to the fraudulent transactions carried out at PNB, closed 5.3 per cent down.
Among other lenders which have said they had exposure to the fraudulent transactions, Union Bank of India fell 7.4 per cent, while State Bank of India closed down 1.2 per cent.
Including direct loans given to companies of Mr Modi and Mr Choksi, Indian banks are at the risk of taking a hit of more than Rs 19,300 crore after the fraud, according to an internal tax department note seen by Reuters.
A finance ministry spokesman, however, said today the tax department had not submitted any formal note on the investigation yet.
"There are many internal investigations going on, there is no note that the department has submitted," the spokesman said, responding to the Reuters story.