Status Yellow rain warnings have been issued for a number of counties this week.
Met Éireann has issued a rain warning for counties Waterford, Wexford and Wicklow, in effect from 12:00a.m until 6:00p.m on Tuesday (January 27).
Outbreaks of rain, heavy at times can be expected.
Possible impacts include localised flooding and difficult travel conditions.
The UK Met Office has issued a Status Yellow rain warning for counties Antrim, Armagh, Down, Fermanagh, Tyrone and Derry.
This warning is in place from 6:00a.m until 3:00p.m on Tuesday.
Outbreaks of rain may lead to some flooding and disruption, the Met Office said.
Widespread rain
Met Éireann said today (Sunday) will be cloudy for most of this morning with some mist and fog in places, along with scattered outbreaks of rain and drizzle, heavy at times and most frequent in the north and north west.
It will become drier this afternoon with some bright spells around and just scattered patches of light rain or drizzle.
There will be highest temperatures of 5° to 9°, in light to moderate easterly or variable winds.
Rain and drizzle will continue overnight with dry and clear conditions over parts of the south west where frost and icy patches may form early on in the night.
Cloud will thicken towards morning as heavy rain feeds in from the south west.
There will be lowest temperatures of 0° to 5°, coldest in the south west.
Monday will be another dull and wet day with widespread rain.
This will persist for the afternoon, and turn heavy at times, before gradually clearing eastwards.
It will be breezy too with fresh to strong south east winds, and gusts along Atlantic coasts.
Areas of low pressure will bring a continuation of unsettled weather throughout next week, Met Éireann said.
It will be cold and breezy at times with further bands of heavy rain, possibly turning wintry at times.