Nirav Modi, who holds an Indian passport, left India on January 1, while his brother Nishal, a Belgian citizen, departed from the country on same day.
However, whether they travelled together has to be probed, they said.
Nirav Modi's wife Ami, a US citizen, left on January 6 and his uncle and business partner Choksi, the promoter of Gitanjali jewellery chain, left on January 4, the officials said.
The bank claimed that it became suspicious only on January 16 when the accused companies --Diamond R US, Solar Exports and Stellar Diamonds (all accused in the CBI FIR) -- approached it with import documents and a request to issue Letters of Understanding (LoUs) for raising buyers' credit for making payments to the overseas suppliers.
The bank, however, could not find any past entries in the system, the FIR has alleged.
It approached the CBI on January 29 with a complaint of Rs 280 crore fraud, officials said.
The agency immediately swung into action, registering an FIR on January 31, followed by searches at 20 locations in Mumbai and Surat. It also issued a look out circular on February 4 against Nirav Modi and three absconding accused, they said.
A look out circular is issued by enforcement agencies to all exit and entry ports to inform them about the movement of an accused.
Nirav Modi, a regular on the lists of rich and famous Indians since 2013, was booked by the CBI, along with wife, brother and business partner and Choksi on January 31, for allegedly cheating the state-run Punjab National Bank to the tune of Rs 280 crore.
The bank again approached the CBI within a fortnight of the first complaint giving details of more transactions which were over Rs 11,400 crore.
The question as to why the PNB did not send a complaint to the CBI and decided to give it in tranches is also under the scanner of the agency, they said.
The bank has claimed in three complaints to the CBI that so far it has detected 150 LoUs which were fraudulently issued by its officials in connivance with Nirav Modi and the other accused in the case, the officials said.
The agency is analysing the fresh complaints and will take a call whether to register fresh FIRs or expand the ambit of the existing FIR related to fraudulent transactions of worth Rs 280 crore, they said.
The PNB has claimed in the complaint that overseas branch of banks used the funds to clear their own liabilities, the officials said.
During searches conducted by the agency which included the residences of Nirav Modi and the other accused along with companies, the CBI recovered 95 crucial documents related to import bills, they said.
The agency has also seized computers and other digital devices and has completed mirror imaging of computers seized during the searches, the officials said.
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