A Met Éireann status-yellow rain warning issued for Wednesday has been extended to cover 17 counties.
The warning – for Leinster, Cavan, Monaghan, Cork, Tipperary and Waterford – comes into effect at 11pm on Tuesday and runs until 11pm on Wednesday.
The forecaster said rain falling on already saturated ground and high river levels could lead to flooding. It also expects poor visibility and difficult travelling conditions.
A yellow wind warning is also in place for Wexford, Wicklow, Dublin, Meath and Louth from 11pm on Tuesday to 1pm on Wednesday.
Met Éireann said strong and gusty south-easterly winds combined with high tides may lead to wave overtopping, fallen trees, loose debris and difficult travelling conditions.
Tuesday started out brightly but cloud is forecast to thicken through the day. Outbreaks of rain and drizzle are to spread across Munster from the southwest in the late morning and afternoon. Highest temperatures of between 3 and 7 degrees are forecast.
Conditions are to become wet and windy overnight with outbreaks of rain becoming widespread, and possibly falling as sleet or snow at times, in the west, northwest and on higher ground.
Wednesday will be wet and breezy with widespread outbreaks of rain and drizzle, possibly falling as sleet or snow in the northwest and on higher ground. The rain will gradually become confined to Leinster and Ulster, with scattered showers in Connacht and Munster.
Thursday will start off mostly cloudy, but scattered showers or more persistent spells of rain will move north-eastward across the country. Drier and brighter conditions are to follow from the southwest. Highest temperatures will be between 5 and 10 degrees, coolest in the north and mildest in the southwest.
Conditions will remain mixed on Friday with outbreaks of rain and showers, heavy at times, spreading eastward across the country. Some brighter spells will develop in the afternoon. Highest temperatures of between nine and 12 degrees are forecast.
Saturday is expected to be a breezy day, with current indications that outbreaks of rain and drizzle will become patchier as they clear northwards.
The weather is to remain unsettled for the remainder of the weekend and into next week, with Atlantic low pressure remaining dominant.