A Status Yellow rainfall warning for Connacht, Longford, Offaly, Westmeath, Cavan, Monaghan, Clare, Cork, Kerry, Limerick and Tipperary will remain in place until noon.
Met éireann said the rain may lead to spot flooding in places - with 25mm to 35mm expected.
The rain may turn to snow in parts for a time.
TODAY
It will be wet and blustery across much of the country this morning with further spells of rain and strong and gusty west to southwest winds.
Any snow across Ulster will turn back to rain.
The rain will clear in the early afternoon with sunshine and scattered showers of rain, hail and sleet to follow with some snow on higher ground again later.
Afternoon temperatures will range from 3C or 4C in the northwest to 6C or 7C in the south.
TONIGHT
Tonight, wintry showers will continue for a time with possibly some snow on higher ground.
Lowest temperatures of between -1C and 3C degrees with some frost further inland and a risk of icy roads.
Westerly winds will be mostly moderate.