The action has been taken on a complaint by the bank on March 4, they said.
The CBI has named Modi, then president (finance) of his Firestar Diamonds International Limited Vipul Ambani, chief finance officer Ravi Gupta, other directors and officials of the company, and unidentified public servants of the bank, they said.
This is the second CBI FIR in which Modi has been named.
The bank has alleged in its complaint that its Brady Road branch in Mumbai had extended credit facilities to Firestar group between 2013 and 2017.
In its compliant, now part of the FIR, the bank alleged that it came to its notice that credit facilities were not used for the purpose -- packing credit, guarantees etc -- for which they were given.
The bank alleged that during its internal investigation, it spotted "circular transactions" between Modi promoted partnership firms -- Solar Exports, Stellar diamonds and Diamond R Us -- and Firestar group of companies, also promoted by him.
The bank said a criminal conspiracy was hatched by the accused causing a loss of Rs 321 crore which remained outstanding to the public sector bank.
Modi is already facing an FIR pertaining to over Rs 6,200 crore of alleged fraudulent letters of undertaking (LoUs) and Leters of credit (LCs) issued to his company by the PNB.
Modi and his uncle Mehul Choski promoter of Gitanjali group are accused in the issuance of LoUs and LCs worth USD 2 billion (approximately Rs 12,636 crore).
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