Italy's data protection authority said Intesa Sanpaolo had underestimated the seriousness of a data breach incident involving thousands of customers, widely reported to include Prime Minister Giorgia Meloni.
Last month, the authority asked the bank to provide clarification over the case involving an Intesa employee who allegedly accessed the data of about 3500 clients.
Intesa said in a statement that further checks had shown the number of customers affected was "significantly lower than previously reported in the media".
The data protection watchdog instructed the bank to inform all customers whose data has been violated within 20 days.
Intesa first suspended and then dismissed the employee who spied on the accounts.
On uncovering the breach and conducting a preliminary audit, Intesa had informed the data protection authority of the incident, while filing a complaint with prosecutors.
After going through the procedure, it was allowed to sack the employee.
But the authority said in a statement that the bank had not adequately informed it about the extent of the breach, which became apparent later due to press reports and was only confirmed subsequently by Intesa.
"Contrary to the bank's assessment... the breach of the personal data represents a high risk for the rights and the freedoms of the individuals concerned," the authority said.
It said the potential consequences of the breach had included disclosure of information on the financial status of individuals and reputational damage.
The authority said it would assess the adequacy of the security measures the bank has put in place and ordered it to provide feedback within 30 days.
Intesa said it had already started working to respond to the authority's requests.
Ensuring the highest level of security for its customers' data was a priority, it said, adding that it had already enhanced its systems and control procedures.
Intesa also said there was no evidence the data had been shared outside the bank.
