Some 130,000 people remain without power and tens of thousands without water in the wake of Storm Ophelia.
Energy chiefs in ESB Networks warned that progress to reconnect remaining homes, mostly in the south of the country, would take several days.
“As we move down to lower voltage repairs this work slows down as individual faults are repaired,” the company said.
ESB Networks is also prioritising power connections to water treatment and supply plants after the storm wiped out services to tens of thousands.
About 48,000 Irish Water customers remain with no supplies.
ESB Networks said it had restored power to 255,000 of those who had been cut off during the hurricane-force winds on Monday.
It could be another week before some homes see the lights come back on.
People in the worst affected areas, from Wexford to Skibbereen in Co Cork, have been asked to conserve water supplies as far as possible while repair work continues as reservoirs refill and pumping systems get back to full operation.
Soldiers have been deployed in the Republic, along with two military vehicles and two helicopters to help assess damage as thousands of ESB staff work to fix fallen and broken cables.
Workers in Kilcock, Ireland, clear fallen power lines (Niall Carson/PA)
Crews from Northern Ireland joined efforts on Tuesday night and others from Scotland and France are expected to be drafted in on Wednesday.
Northern Ireland Electricity said about 270 homes and businesses in the Newry, Downpatrick, Bangor, Portavogie, Newtownards and Dunmurry areas were without power following Storm Ophelia.
Schools across the Republic have reopened after two days because of the threat from power outages and risks to travel at the height of the storm.
Three people died when the ex-tropical storm, the strongest system to hit Ireland in almost 60 years, battered the country on Monday.
Father-of-two Fintan Goss, 33, was killed in Ravensdale, Dundalk, when a car he was in was struck by a tree 10 minutes from home on Monday.
Ophelia battered the UK and Ireland with gusts of up to 80mph (Niall Carson/PA)
Louth county councillor John McGahon described Mr Goss, who he said became a father for the second time in recent weeks, and his family as “extremely well-regarded in the community”.
In Cahir, Co Tipperary, 31-year-old Michael Pyke was killed in a chainsaw accident when he was trying to clear a tree downed by the wind.
Former oncology nurse Clare O’Neill, who was just short of her 59th birthday, died when a tree fell on her car in strong winds near Aglish village in Co Waterford.
About 110,000 homes and businesses are also without broadband, landline and mobile access.
Eir said the South West and Midlands were the worst affected areas, particularly Co Cork.
The company said the numbers affected would drop throughout the day as power supplies were restored but it also warned that it would see an increase in the number of individual line fault reports.
Eir warned it had taken 400 reports of dangerous lines and telegraph poles and that damage was extensive and the repairs would take time.