Communities have been warned that further flooding was possible over the weekend, following heavy rains associated with Storm Claudia overnight.
Flooding was reported in Portarlington, on the border of counties Laois and Offaly, despite no rain warning being issued for those counties, as well as in Co Wexford.
Thousands of homes and businesses were left without power as rain weather warnings were lifted in the south-east this morning.
The National Directorate for Fire & Emergency Management (NDFEM) held a meeting of local authorities, relevant government departments, state agencies and utility providers this afternoon to discuss the response to the heavy rain.
It said the impacts of heavy rain will continue in parts over the weekend, with further flooding possible in Leinster and Munster as some rivers had not yet peaked.
As there had been rainfall in previous days, many grounds are "already saturated", it said, adding that many rivers were "at capacity".
The Department of Social Protection has activated the relevant flood relief humanitarian assistance scheme for households affected by the weather event, and the Department of Enterprise is liaising with local authorities about the activation of the scheme to help businesses.
Watch: Drone footage shows extent of Portarlington flooding
Eighteen properties were flooded across Co Wexford overnight. Half of the flooded properties were in Bridgetown where a canal burst its bank causing damage to a number of properties, including a business.
Five properties were flooded in the Gorey area when the River Ounavarra burst its banks while there were also incidents in Castlebridge, Mayglass, Mauritiustown and Newline Road.
Crews from Wexford County Council and the local services responded to the incidents.
In Co Laois, parts of Portarlington were under water after levels in the River Barrow peaked at around midnight last night.
Some roads and the People's Park in the town are flooded, but no properties were impacted by the flood water.
Senior Assistant Chief Fire Officer for Portarlington Anthony Tynan said the situation has improved considerably from yesterday, and that the work of the council and local fire services had prevented and homes and businesses from flooding.
"We've had steady rainfall over the last three or four days and it's been a cumulative event rather than a single once off. For the last few days, the council's severe weather assessment team has been meeting twice a day to see what's happening on the ground and make preparations".
Watch: Flooding in Portarlington's People's Park
Keith Leonard, national director of the NDFEM, said people should be aware of the conditions in their area.
"River and surface water flooding has occurred in some areas in Leinster and Munster today, due to the rainfall yesterday and earlier this week, which has led to saturated grounds and swollen rivers, some of which have broken their banks.
"We are asking people to drive with extreme caution and be aware of the local conditions which will vary from place to place depending on the level of flooding.
"We continue to ask people to avoid open riverbanks and canal paths in flood conditions, and to stay away from swollen rivers, streams and flooded riverbanks, where banks can collapse without warning.
"Flooding impacts can be very localised and specific, so be sure to heed any advice issued by the emergency services and your local authority.
"Drivers also need to be aware of potentially hazardous conditions in their local area, so please slow down, increase stopping distances and watch for surface water and debris on roads.
If the road ahead is flooded, do not enter - turn around and find another route," said Mr Leonard.
A spokesperson for the ESB said the storm brought a "modest impact" to electricity infrastructure in line with previous wind warnings.
By 6pm this evening, the number of homes, farms and businesses without power was down from several thousand to the "low hundreds", according to the spokesperson.
A Status Orange rain warning was in place for counties Dublin, Wexford and Wicklow until 8am this morning, while a Status Yellow rain warning was in place in 10 other counties, mostly along the east and south coasts, until 9am.
In Northern Ireland, a yellow-level rain warning was in place in counties Armagh and Down until noon, bringing a risk of flooding and hazardous travelling conditions.
Watch: River Dodder in Dublin swells after heavy rainfall
In Dublin, the City Council said it is continuing to monitor the River Dodder after rainfall in the Dublin Mountains exceeded 100mm since yesterday and localised flooding in the Dartry and Milltown areas following a substantial swell.
"Flood defence gates remain in place along the lower Dodder near the Aviva Stadium and will be reviewed later today ahead of the Ireland vs Australia rugby fixture at 8pm, which coincides with the evening high tide."
It said 70 flood response staff are operating city-wide and flows on the Rivers Dodder, Camac and Poddle are being closely monitored.
Dublin's three other local authorities Fingal, South Dublin and Dun Laoghaire Rathdown and Dublin Fire Brigade had crews working overnight who responded to a number of minor incidents involving surface water and fallen trees.
Stena Line said a number of its ferry services on its Dublin to Holyhead route have been cancelled and will resume when safe to do so.
Dublin airport operator daa is expected to run a full schedule today.
Passengers have been advised to check ahead with their providers.
Gardaí have appealed to road users not to be complacent this afternoon and evening, even though the worst of the weather has passed; but to "expect the unexpected".
Superintendent Liam Geraghty from the Garda Press Office said the road network is "extremely wet and saturated" and that rural and less-travelled roads will be covered with leaves and debris, and possibly even trees that have fallen down.
He urged motorists to be cautious, slow down and leave plenty of time to brake.
Supt Geraghty also warned that the rain from the last 24 hours is still making its way down into water networks and drains and could still cause localised flooding.
Additional reporting: PA
