ESB Networks has said approximately 39,000 premises remain without power across the country, a reduction of around 6,000 since last night.
It said it has restored power to 729,000 homes, farms and businesses since Storm Éowyn brought high winds that caused widespread damage to the network.
The electricity utility company said restoration work is continuing, adding that some customers may see changes to their estimated power restoration times, specifically in the areas with the largest number of faults.
Those still without power, it said, "will progressively have their supply restored over the course of next week".
It warned that customers whose electricity has been restored should be aware that supply may be disrupted for "very short periods of time" to allow others to be reconnected.
Restoration efforts in the worst impacted areas are being aided by technicians from Austria, Finland, France, Great Britain, Germany, Netherlands and Norway, it added.
Approximately 1,600 customers remain without power in Northern Ireland.
NIE Networks said it had over 1,550 staff and contractors escalated along with additional support from other countries and further support on the way in response to the outages.
Power outages peaked at 285,000 in Northern Ireland as a result of Storm Éowyn.
NIE Networks also said it was aware of reports of people calling to properties claiming to be from NIE Networks.
It said its staff will always carry ID and asked the public to report any suspicious activity to the PSNI.
Yesterday, opposition parties in the Republic called for State supports to be made more readily available and for increased finance to be provided to local authorities for preventative measures surrounding storms.
Sinn Féin sought the distribution of goodwill payments to households who have been without power, saying this should be funded by energy companies.
