The three fraudulent remittances were sent via correspondent banks, to accounts in Dubai, Turkey, and China.
"The incident that happened in our bank is because of the cyber-attack initiated by the global cyber criminals and there is no evidence of internal staff involvement", the City Union Bank said in a statement.
The bank had been able block only one of the transfers worth $500,000, while attempts were under way to retrieve the rest, he said.
It has not disclosed any details regarding the possible perpetrators behind the cyber heist.
In recent years, hackers have targeted a slew of banks worldwide to gain access to the Swift network and initiate fraudulent money transfers. Bank officials in Dhaka initially assumed there was simply a printer problem.
The remittances were sent via the popular Swift platform, which was notoriously abused by suspected North Korean hackers to pull-off an audacious $81m cyber-heist at the Bangladesh Bank back in 2016. The money was sent to accounts at Manila-based Rizal Commercial Banking Corp and then disappeared into the casino industry in the Philippines.
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"We definitely see similarities between the Bangladesh case, and the similarities are being factored into the investigation", Kamakodi said.
"The volume of unsanctioned operations as a result of this attack amounted to 339.5 million roubles", the central bank said without naming the institution involved or specifying when the attack took place.
The first fraudulent transaction detected by City Union Bank consisted of Dollars 500,000 bound for a Dubai-based bank.
"It's a cat and mouse game", he said.
On Sunday, the CEO had said "cyber criminals" had hacked its systems and transferred almost $2 million via unauthorised remittances to lenders overseas through SWIFT financial platform.
Natasha de Teran, a spokeswoman for Swift, said the firm does not comment on individual entities but emphasised that its systems have never been compromised by hackers.