Eircom says its services have stabilised this evening and customers should now be able to make and receive calls without disruption.
A fault on the company's core telephony network caused problems for some mobile and landline calls for several hours today.
Eircom said about 5% of its total network traffic was affected.
The situation primarily affected business customers, including companies using 1800 and 1500 numbers, and people trying to call those numbers.
Mobile customers were also affected.
A spokesperson for Eircom said businesses with complex telephony systems were particularly affected.
The spokesperson said calls were now being connected, and Eircom was still working to investigate the root cause of the problem.
The spokesperson said Eircom would provide telecoms regulator Comreg with an incident report in relation to the situation, and that this was standard practice where its service had experienced disruption.
Comreg said it was engaging with the company and would be seeking a full incident report from it.
Earlier, the Health Service Executive said Eircom confirmed that all 1890,1950, and 1800 numbers in Dublin, including the medical card line were restored.
A HSE spokesperson said that the ambulance service has secondary back-up lines and TETRA radio to communicate with hospitals directly so no issues had arisen as far as they were aware.
She said they had asked their call centre staff to be extra vigilant and take down a mobile number for all callers.
Childline said via Twitter that children trying to contact it may experience problems because of the Eircom issues and said they should go to its website for help.
Gas Networks Ireland said the outage might have affected customers using the 1850 20 50 50 number to report issues and advised people to contact its temporary emergency numbers - 087 9160734 or 087 9160701 - to report a gas leak.
Calls from eMobile or the Meteor network to 1890 260 260, Broadband Tech Support or to 1800 numbers were not being connected.
The issue, which began just before 10am, had also hit calls to Eircom’s customer care centres.
Speaking on RTÉ's News At One, Eircom Director of Corporate Affairs Paul Bradley said the disruption had impacted some of its business customers, those trying to reach 1800 and 1500 numbers, and businesses that have complex telephony systems, where they are trying to dial out.
Dublin Fire Brigade said in a tweet during the outage that it had been advised by Eircom that using landlines to contact emergency services "may be difficult".