Met Éireann has warned that strong winds are likely to sweep across parts of the country again tonight.
The forecaster said westerly winds would increase to gale force levels and gusts of 100 to 120 km/h were to be expected in upland and coastal areas of Connacht and west Ulster until tomorrow morning.
Met Éireann also said winds could reach storm force 10 on coasts from Slyne Head to Malin Head to Carlingford Lough and for the north Irish Sea.
Communities along northern and northwestern coasts were hardest hit by the winds yesterday – which peaked at 168km/h in Co Donegal.
The winds caused disruption to power supplies in parts of Dublin, Kerry, the midlands, Wexford and Galway as trees were uprooted and power and telephone lines were damaged.
Some 120 homes around the country were still without electricity earlier today.
ESB said engineers have managed to return power to almost 15,000 homes, but small pockets remain cut off, with Scariff in Co Clare, Carndonagh and Buncrana in Co Donegal, and Bagenalstown in Co Carlow worst-affected.
An ESB spokesman said some households would experience short power disruptions throughout the day as crews work to repair some faults which were temporarily fixed yesterday. “We are expecting more winds today but not like yesterday,” he said. “It is important to get these repairs right so we ask customers to bear with us.”
Members of the public have been asked to contact the ESB's emergency number on 1850 372999 if they come across fallen power lines.
A further 10,000 homes and businesses were affected in the North as Northern Ireland Electricity reported up to 500 faults on its network, with Coleraine, Ballymoney and Bangor among the hardest-hit areas.
Elsewhere, Eircom is continuing to fix more than 5,000 faults reported on its telecommunications network.
Some flights and ferry crossings were cancelled as a result of the high winds and a number of roads were blocked by fallen debris.
The strongest gust of 168km/h was recorded at Malin Head, Co Donegal, early yesterday morning while wind speeds of more than 100km/h were recorded at Belmullet, Co Mayo, and Dublin airport, Met Éireann said.
An Garda Síochána and the Road Safety Authority have urged motorists to take care on the roads while the windy conditions persist.
Road Safety Authority chief executive Noel Brett said yesterday: “I would ask each and every one of you to allow extra time to reach your destination, keep a safe distance from the vehicle in front and adjust your speed in windy or wet conditions.”
Harry Blaney Bridge in Fanad Co Donegal is expected to remain closed to high-sided vehicles, caravans and motorcycles until this evening, because of strong winds. These vehicles can divert via Milford. The bridge is open to cars.