Northern Ireland Electricity (NIE) said it hoped to reconnect power to 10,000 properties on Tuesday.
Hundreds of thousands of homes and businesses were left without power at the height of Storm Éowyn on Friday.
On Tuesday morning the figure was 43,000. However, as of 15:50 on Tuesday, that number had fallen to 37,000.
Specialist engineers have arrived from England to help restore power, but NIE has warned it could be 3 February before all properties are reconnected.
In the Republic of Ireland, more than 140,000 customers remain without supply, according to ESB Networks, down from a peak of about 768,000 properties on Friday morning.
Thousands of trees lost
Meanwhile, the National Trust has said the storm “wreaked havoc” on its estates and gardens in Northern Ireland.
It estimates that 10,000 trees in Mount Stewart in County Down were “flattened” by hurricane force winds
Winds of up to 90mph left Rowallane Garden in Saintfield “almost unrecognisable” with irreplaceable specimen trees permanently lost, some over 250 years old, as well as rare and exotic species and rhododendrons planted by the estate’s former owner, Hugh Armytage Moor, in the 1870s.
Some of the trust’s properties remain closed as the damage is assessed and clean-up works get under way.
Gregor Fulton, trees and woodland adviser for National Trust in Northern Ireland said: “Our ranger and garden teams have been busy assessing the aftermath of the storm, but it’s already clear we’ve lost a large quantity of trees, which is sad, as Northern Ireland is already one of least wooded parts of Europe.
“Mount Stewart suffered devastating damage with thousands of trees down, and at Rowallane Garden, some of the areas are unrecognisable.
“Many of our trees have veteran qualities and important histories, and they connect us to the people who planted them, as well as playing a vital role in the ecosystems of our landscapes.
“At Castle Ward we have lost a beech tree over 200 years old, several from the historic lime tree walk, and an ancient Yew tree.”
In March of last year, work began at a tree nursery at Mount Stewart which aims to produce 600,000 trees per year.
On Tuesday, Communities Minister Gordon Lyons pledged £1m to support communities and individuals affected by Storm Éowyn.
“Storm Eowyn has caused devastation, and my primary concern is the safety and well-being of all those affected, particularly children, the elderly and people with vulnerabilities,” Mr Lyons said.
Lyons said Stormont departments would do everything possible to help support those who have found themselves homeless and for those needing assistance.
Speaking to ‘s Good Morning Ulster on Tuesday, Ronan McKeown from NIE said it was becoming a “trickier picture” to reconnect properties which were still without power.
He added that NIE had “1,000 people on the ground” trying to restore power, 100 of whom were from “overseas” and that 250 generators had been delivered to vulnerable customers.
Asked about compensation payments for people left without power for a prolonged period, Mr McKeown said conversations would continue on Tuesday between NIE and Stormont ministers, the Economy Department and Utility Regulator.
Gary Curran from NI Water said most of the 600 properties without water were in the west of Northern Ireland.
He said his organisation hoped to get generators to a further 17 properties on Tuesday and that 360 vulnerable customers had water delivered to them.
The aftermath of the storm has also affected schools, with some still closed on Tuesday.
Engineers redeployed across UK
More than 400 electricity engineers and field staff have been redeployed across the UK to assist with the clean-up operation.
In a statement, the Energy Network Association said that “nearly 200 staff have been redeployed to Northern Ireland to date, in addition to helicopters, drones, generators and replacement parts from stockpiles in other parts of the UK”.
“The staff have been redeployed from their usual locations – from Plymouth to Newcastle – to work in other areas of the country, where support has been needed the most.”
Jersey Electricity (JE) dispatched a team to Northern Ireland to help power restoration efforts. It said the team of three overhead linesmen and two vehicles left the Channel Islands to assist on Saturday.
JE said the team were providing “on-the-ground support, focusing on repairing overhead power lines and restoring critical supply to affected homes”.
GP surgery reopens
Castledawson GP surgery opened on Tuesday for the first time since the storm.
The practice had no power until Monday night, which meant it could only operate an emergency service via a mobile phone.
Practice manager Sinéad Campbell said the lack of power and heat had a huge impact on the day to day running of the surgery.
“We’re going to have a knock-on effect probably for the next month,” she said.
“There are patients here booked in for routine bloods, injections, vaccinations. Those are all important.
“They’ve missed those. Now were going to have to try and provide a service to get those all caught up over the next few weeks.
“It’s going to mean staff working extra in times when we’re already pushed to capacity.”
Relief for reconnected customers
Gerry Rea, from Bleary near Portadown, has severe mobility issues and was left without power from Friday until Monday evening.
He uses equipment in his home to help him get around, which requires electricity.
“I actually can’t get up off a chair or off a bed, I don’t have the leg capacity to do that on my own,” he told Good Morning Ulster.
“So, when the electricity went on Friday morning, I lost all that capacity and I literally have to be hauled up off the chairs,” he said.
Mr Rea spent Saturday and Sunday in a B&B, which cost him more than £100 per night.
He said he was given conflicting information by NIE over the weekend but was relieved to be back home again after an experience that had left him exhausted.
‘Be wary of rogue traders’
Meanwhile, people who may be in a rush to repair their homes that have been damaged by the storm are being warned not to be scammed by rogue traders.
Damien Doherty, who is chief inspector of the Department for the Economy’s (DfE) Trading Standards Service (TSS), said many rogue traders would seek to take advantage of the damage caused by Storm Éowyn.
Speaking to Radio Foyle’s North West Today programme on Tuesday, Mr Doherty said people, especially the elderly people, could be at risk of being scammed.
“Unfortunately we get complaints about rogue traders calling door-to-door every week,” Mr Doherty said.
“It is very real that we have these rogue traders going around streets and telling people they can see damage to fences and roofs and can do the job quickly and at low costs.
“What happens then is they tell you the price of the job has gone up during or after the work, and the trader can become threatening and quite intimidating and the work – if they do it at all – is to a very low standard.”
Mr Doherty said advice for anyone who has been scammed or to help people spot warning signs can be found on their website.
Emergency contacts
NIE has said there are 11 Community Assistance Centres, external and more than 60 drop-in centres open until 19:00 GMT to help those without power.
Facilities offered range from showers, food, hot drinks, and work-from-home hubs. NIE Networks reps are available for support.
To report faults or emergencies you should contact:
Northern Ireland Housing Executive: 03448 920 901
Openreach Damages to Network: 08000 23 20 23 (Individual faults must be logged with Communications Providers)
Gas networks: 0800 002001
NI Water: 03457 44 00 88 or visit niwater.com, external
Flooding Incident Line: 0300 2000 100
NIE Networks: 03457 643 643 or visit nienetworks.co.uk