Taoiseach Leo Varadkar has said the vast majority of insurance policies are valid for damage from Storm Ophelia.
About 125,000 homes and businesses remain without power, 85,000 are without broadband, landline and mobile access and 58,000 without water in the wake of the storm.
The Taoiseach said Government would engage with the insurance industry in the coming days.
But he urged consumers to read the fine print on policies as well.
"We do think this will be a little bit different to flooding," the Taoiseach said.
"I know that when it comes to severe weather that causes flooding, that quite a number of people find themselves un-insured because they are on floodplains or have been flooded before.
"We expect this will be different. Nobody is in a hurricane path. It's different to a floodplain.
"We think that in the vast majority of cases people will be insured and will be covered but the best thing to do is to read your own policy and contact your insurer as soon as you can."
Energy chiefs in ESB Networks warned that progress to reconnect remaining homes, mostly in the south of the country, would take several days.
Mr Varadkar said that in the wake of Storm Darwin in early 2014 that it was eight days before the network was fully repaired.
It is expected that the majority of the 119,000 customers who remain cut off will have their power restored over the next four days.
"But the company warned that some customers in isolated pockets will not be reconnected until Tuesday.
ESB Networks is also prioritising power connections to water treatment and supply plants after the storm wiped out services to tens of thousands.
Fifty grid repair staff from Northern Ireland Electricity joined efforts on Tuesday night and teams from Wales, Scotland, the Isle of Man, northern England and France will begin working on lines on Wednesday and in the coming days.
An ESB Networks spokesman said: "As we move down to lower voltage repairs this work slows down as individual faults are repaired."
The company also began posting estimated power restoration times on its Powercheck app and powercheck.ie.
By lunchtime on Wednesday Northern Ireland Electricity said fewer than than 150 homes and businesses remained without power in its region.
Schools across the Republic also reopened after a two-day shutdown 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.
Meanwhile, agriculture chiefs urged co-operatives to co-ordinate efforts and keep dairy farms running through black-outs.
Sean O'Leary, national dairy chairman of the Irish Farmers' Association (IFA), said the most pressing problem was the welfare of herds and protecting milk supplies.
He said: "Ensuring that cows can continue to be milked is crucial from an animal welfare point of view, and maintaining refrigeration is essential to ensure the valuable quality milk produced is not spoilt or wasted."
Some co-ops, including Glanbia, have arranged teams of electricians and are ensuring generators are moved to where they are needed most, the IFA said.
Mr O'Leary added: "It is essential that co-ops would co-ordinate their efforts, especially in the South West, the South East and the West, where the impact from Ophelia on the power grid seems to have been the greatest."