Eircom is strongly recommending that its 350,000 email customers change their account passwords today and on a regular basis in the future.
The advice follows the attempted hacking of the eircom.net email system.
The email service was temporarily shut down last night as a result of the attack.
It is gradually being brought back online today.
The company said the attempted intrusion was detected on the perimeter of the email service, but would not say what the nature of the attack was.
Eircom said it has no evidence so far to suggest that the system has been compromised.
It also said it has no evidence to suggest other Eircom systems or data have been compromised.
However, it has alerted the relevant bodies as a precaution, including the Data Protection Commissioner, ComReg and the Department of Communications.
Eircom said staff worked overnight to implement a number of system modifications and it expects all customers to have access by this evening.
All pending email traffic has been stored and will be delivered as soon as possible. Eircom apologised for the inconvenience caused.