Customers are being asked to conserve supplies where possible
Irish Water says it is "aware" that some people were without water entirely overnight.
The utility says it is is working as part of the National Emergency Committee (NEC) and local authorities to restore full supply.
It says the supply has had to be restricted or cut off due to an increase of over 10% in demand from the the Greater Dublin Area over the weekend.
"Despite having our plants working at peak output, storage of water in the reservoirs was significantly depleted", it says.
"Irish Water had to act to protect homes and businesses in Dublin and avoid widespread outages in the capital."
"The decision to reduce pressure across the Dublin network for a 12 hour period was one that was not taken lightly but we needed to ensure the city continued to function."
In Dublin water pressure has been increasing since 7am. It may take some time for everyone to see the increase as water travels through the network. Please bear with us. It is important to continue to conserve water during the day where possible. https://t.co/SzaMPXTWMm— Irish Water (@IrishWater) March 6, 2018
"Irish Water recognises that many of our water customers continue to face severe impacts from water interruption or restrictions, where customers only have water at certain times. These are likely to continue for a number of days."
It says it is aware that some people were without water entirely and is reviewing the situation with water engineers to see how they can minimise this impact.
It adds that hospitals on the network will be prioritised and have water diverted to them.
It also says that "significant progress" has been made to make necessary repairs at plants and fix bursts.
In all, just over 20,500 people are without water and an additional 47,000 have restricted supply due low levels in reservoirs.
Those without water are include almost 2,000 in Cork, 7,300 in Wexford and 12,250 in Tipperary.
Those on restricted supply include 500 in Cork, 16,500 in Galway, 300 in Kildare, 16,500 in Leitrim, 700 in Mayo; and 12,500 in Meath.
The utility is also examining a shorter restriction plan:
They are looking at a shorter time frame of 8pm to 6am in order to ensure people do have a water supply in the morning. Irish Water apologizes to those hit today— Sean Defoe (@SeanDefoe) March 6, 2018
Nighttime restrictions or loss, mainly around Dublin, followed a huge increase in demand over the last week.
Customers are now being asked to conserve supplies where possible.
Eamon Gallen from Irish Water says they are trying to limit disruption.
"Over the course of the morning supplies will come back.
"We will probably have to introduce restrictions for a number of weeks, if not months, to come.
"But we will try and minimise the impact on customers by doing them out of hours at night, where possible, and generally people will not be affected".
Meanwhile Irish Water says it may be a number of days before a safe supply is restored to hundreds of homes in part of south Tipperary.
It is after a major spillage of Kerosene oil contaminated supplies the Fethard public water supply.
Irish Water has issued a Do Not Drink notice, but the water can be used for washing.
The utility says it may be a number of days before a full supply is restored.
Additional reporting: Jack Quann