Eircom crews have been working throughout the weekend to repair faults caused by bad weather conditions last week.
Both broadband and telephone services have been impacted.
Counties Wexford, Carlow, Kilkenny, Cork, South Kerry, Clare, Galway and Mayo are the areas which have been most affected.
Spokesperson for eircom, Paul Bradley, said their crews are working to reconnect customers as quickly as possible.
"This morning we have approximately 4,500 faults," he said.
"Yesterday we cleared an re-connected service to more than 1,200 customers, and our crews will be out working today to connect as many customers back to the network as quickly as they can."