Met Éireann has issued a warning for Cork, Kerry and Waterford
€8m in government funding is being allocated to Local Authorities to help the cost of the clean-up in communities hit by flooding.
For the first time in two weeks, National Emergency Co-ordination group reported that water levels along the River Shannon have not risen.
However, the group says there is still a significant flooding situation and also a need for the continued use of water pumps and flood defences.
Persistent and heavy rainfall over the past week and a half has left many homes and businesses in the west, south-west and midlands devastated by flooding.
It comes as Met Éireann has issued a yellow rainfall warning for Cork, Kerry and Waterford.
It says rainfall totals of between 25 and 30mm will fall during Tuesday.
But Jim Casey from the Office of Public Works (OPW) says some water levels around the Shannon have fallen in the past 24 hours.
It comes after the ESB said there will be no change to flow of water downstream of Parteen Weir. It said the rate of flow will remain at 440 cubic metres per second.
The level in Lough Derg has remained constant in the last 24 hours.
Although the weather forecast is mixed, ESB says it expects that the current level of 440 cumecs can be maintained and expect that no further increases in flow will be required over the next couple of days.
"This will depend on the actual rainfall and the situation will be reviewed again tomorrow", it adds.
This level of water flow is likely to continue to have associated flooding to land and property in the vicinity of the Shannon downstream of Parteen Weir - including the areas of Springfield, Montpelier, Castleconnell, Mountshannon (Annacotty) and the University of Limerick.
A €5,000 scheme has been made available to small businesses who have been affected by flooding.
The application process, which is being administered by the Red Cross, opened last Friday.
Chief executive of the Irish Red Cross, Liam O'Dwyer, says they have received some applications as well as a lot more phone and e-mail queries.
Meanwhile, local authorities in Limerick are calling for an immediate review of the management and operation of the Park Canal by Waterways Ireland.
Fourteen homes were flooded in Corbally at the weekend as council workers struggled to open the canal lock.
Waterways Ireland says it left keys for the lock with the Council and relevant phone numbers.
But in a statement, Limerick City and County Council says the keys did not open the gates and Waterways Ireland were not immediately available.
While the Public Expenditure Minister Brendan Howlin has said there is merit in examining the idea of a single agency to monitor the River Shannon.
In the year 2000, Longford–Westmeath TD Willy Penrose proposed a bill for the formation of a River Shannon Authority.
Deputy Penrose renewed his calls for a single River Shannon Catchment Authority following severe flooding in 2009.
Earlier, Minister Howlin said a more coordinated approach to the flooding risks around the Shannon.