Counties Waterford, Wexford, Wicklow, Carlow, Cork and Kilkenny will be under the warning from midnight tonight until midday on Tuesday.
The national forecaster has warned that downpours could cause localised flooding, difficult travelling conditions and poor visibility.
A Status Yellow rain warning was in place for most of today for four counties in the west.
The warning for counties Clare, Kerry, Galway and Mayo was in place from 8pm on Sunday and expired at 8pm this evening.
Heavy rain spread from the west today with dull and blustery weather, accompanied by outbreaks of rain, heaviest across the western half, with ongoing potential for localised flooding.
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Tonight will see outbreaks of rain continuing in Munster and south Leinster, which might turn heavy in places.
Elsewhere will enjoy drier and clearer conditions, with some showers expected, as temperatures drop to 10 and 14C.
Tomorrow might continue to bring rain spreading northwards across the country in the morning and afternoon.
The rain will clear northeastwards to some scattered showers in the evening.
The highest temperatures on Tuesday might reach 16C in some places, with winds easing later.
Stock photo: AP Photo/Michael Probst
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Tuesday night will stay clear and might bring some showers at first, but will turn cloudier overnight with rain and drizzle spreading from the south.
Meanwhile, temperatures will drop to 8 and 12C, and it will be even milder in the southeast.
Met Éireann meteorologist Aoife Kealy said the “unsettled conditions will continue” for the rest of the week, with “frequent spells of wet and blustery weather”.
“It is going to be relatively mild, though,” she added.