Around 142,000 customers are still without power following Storm Éowyn, according to ESB Networks, down from a peak of 768,000.
The ESB has also said that 3,000 electricity poles across the country must be replaced while 900km of new cable must be laid.
In Northern Ireland, around 37,000 homes and businesses are still without power.
Work is also under way to restore water to around 31,000 people who remain without supply, according to Uisce Éireann.
It said a further number of people are at risk of losing supply in areas where treatment plants do not have power but reservoirs still have stores of water.
Storm Éowyn brought record-breaking gusts of 183km/h to Ireland last Friday.
We need your consent to load this rte-player contentWe use rte-player to manage extra content that can set cookies on your device and collect data about your activity. Please review their details and accept them to load the content.Manage Preferences
Meanwhile, the Minister for Social Protection, and Rural and Community Development, has urged anyone in need to come forward and avail of assistance from the State.
"Funds are available, I just want to really emphasise - through the Department of Social Protection. They're doing fantastic work and are extraordinary experienced. We had 1,000 queries yesterday for humanitarian assistance," said Dara Calleary.
"People should not be hungry or cold," he said.
Mr Calleary said there are two elements to the assistance: urgent aid for food and basic needs, and supports for people who have suffered infrastructural damage to their home.
'We have stood up the scheme. You know, we are engaging with people," he said.
The Minister said the State has applied for funding from the EU and said the EU Commission was put on standby that Ireland would need assistance last week.
However specific requests cannot be put in until the damage has been assessed, he said.
Mr Calleary said the severity of the storm was not predictable. We will learn from it though, he said, particularly in terms of communication.
The Minister added that €30 billion extra will be invested in capital over the next five years and he will be looking to ensure that this goes into rural areas.
Mr Calleary said the emergency coordination group has been meeting since Wednesday and as soon as the red warnings were lifted, local authority and ESB crews were out inspecting and dealing with damage.
"I know it doesn't mean anything if you aren't yet reconnected, but every effort has been made and over half a million premises have had power reconnected since Friday," he said.
Taoiseach Micheál Martin has been accused of failing to plan properly for Storm Éowyn by a woman who has been without power and water for days.
Repair crews from Austria and Finland to help restoration efforts
ESB Networks Regional Manager Siobhán Wynne said crews from Austria and Finland will be helping to restore power to the worst-affected areas. They will be deployed to areas in the north of the country.
Ms Wynne said Austrian crews who arrived in Ireland this morning were due to be "up and running by this evening" while Finnish crews, also due to arrive today, will be ready to work by tomorrow morning.
Ms Wynne said the additional resources will deployed across the northwest: "Spanning across from Cavan, Monaghan, across to Longford, Roscommon, Mayo, Galway, up into Sligo and Donegal."
We have freed up all of the crews possible, she said, and we have drafted in timber cutters from the UK to assist in efforts as well.
Ms Wynne said the ESB wants to be as realistic as possible with people and while the return times for power may change, right now, the time frames are "the reality".
The majority of ESB customers impacted by the storm will have their power restored by Friday. However, the ESB said that around 100,000 customers could remain without power into next week.
Elsewhere, the European Union is sending 17 power generators to Ireland to help with the power outages.
Thirteen of the generators will come from the EU's strategic reserve based in Poland, and Denmark has mobilised an extra four via the EU's Civil Protection Mechanism, according to the European Commission.
Members of the public have been urged not to approach any fallen wires and to report any damage to electricity infrastructure to 1800 372 999.
A storm without precedent - Minister
Meanwhile, Minister for Housing, Local Government and Heritage James Browne said the capacity is simply not there to restore all services within a short-time period after an unprecedented storm.
"This has been a storm without precedent. It has been the most damaging, the most dangerous and a most destructive weather event on record in Ireland," he said.
The minister said a review will be undertaken of the storm to see what lessons can be learned for future events.
The Government has said 16 "emergency response hubs" are up and running across the country.
They are in Cavan, Cork, Donegal, Galway, Laois, Leitrim, Limerick city and county, Longford, Meath, Monaghan, Offaly, Roscommon, Sligo, Westmeath, Wexford and Wicklow.
The National Emergency Co-ordination Group said the hubs will support people with "basic needs such as water, hot food, phone charging, broadband access, shower and clothes washing facilities".
Its chair Keith Leonard said the priority for the emergency response is to reach out to vulnerable people impacted by the storm.
Mr Leonard also said there will be a review of the response to Storm Éowyn and the "unprecedented winds" experienced.
He said the review will include a look at the emergency infrastructure including the availability of generators.
Elsewhere, opposition politicians have been calling on the Taoiseach to reconvene the Dáil to address the crisis facing the country in the aftermath of the storm.
