ESB Networks has said its crews and partner contractors are working to restore power to thousands of customers following Storm Darragh.
The supplier said the scale of damage caused by the storm has had an extensive and widespread impact on the electricity supply.
It said the number of customers affected by supply disruption had fallen from yesterday's peak of 395,000.
Around 35,000 customers were still without power at 5pm today as ESB reconnected 360,000 customers so far.
However, ESB warned that a "significant number" of homes and businesses could remain without supply over the coming days due to the severity of harm caused by the adverse weather conditions.
Meanwhile, Northern Ireland Electricity Networks (NIE Networks) said 15,000 remained without power at 9am. They have indicated it may take a number of days to reconnect those customers.
Network operations manager Alex Houston said engineers are working to restore customers as quickly as possible.
"Most of the faults affecting high numbers of customers have been repaired which has allowed us to restore significant numbers of customers," he said.
Separately, mobile and broadband provider, eir said Donegal and Mayo were the hardest-hit counties in terms of outages but service disruptions were felt nationwide.
"More than 35,000 broadband faults, 20,000 fixed voice issues and approximately 15% of mobile network site outages have been registered," it said.
Status Red and Status Orange wind warnings had been issued by Met Éireann as the storm bore down on Ireland on Friday night.
Met Éireann recorded gusts of 141km/h at Ceann Mhása in Co Galway at 11pm, while gusts of 120km/h were recorded at Shannon, Co Clare, and gusts of 115km/h were reported in Co Cork.
Transport across the island was disrupted as flights and ferry sailings were cancelled. Train and bus schedules were also disrupted by the high winds and fallen trees.
