A Status Yellow rain warning is currently in place for counties Carlow, Kilkenny and Wexford until 8am this morning.
Met Éireann also issued a Status Yellow rain warning for County Wicklow which is in place until 9am.
The same alert is in place for Louth until midday.
The forecaster warned the heavy rain may cause localised flooding in the impacted counties.
In Northern Ireland, the UK Met Office issued a Status Yellow rain warning for Antrim, Down and Armagh, which is in place until midday.
The Met Office said the heavy rain may impact the affected areas.
It comes as a Status Orange rain warning for Cork and Waterford and a Status Yellow rain warning for Cork, Kerry and Waterford have both expired.
Met Éireann had warned of heavy rain and possible thundery downpours during the Orange warning in Cork and Waterford, adding that it could contribute to very difficult travelling conditions.
Senior forecaster Gerry Murphy said that there was a very heavy band of rain moving up over the country last night but will gradually clear today.
Mr Murphy also stressed the possibility of river flooding, especially on higher ground in mountainous areas, particularly in west Cork and possibly east Kerry.