NI Water said its staff are work working "day and night" but some customers in more rural areas, including parts of Co Tyrone and Co Armagh, have been affected by supply shortages.
According to the Irish Independent, Irish Water is also due to decide tomorrow if they'll take a tough stance on enforcing the water conservation order.
The areas affected include Lahinch, Lisdoonvarna, Doolin, Liscannor, Ballagh-Cahersherkin and surrounding Group Water Supply schemes.
She warned if demand was not reduced over the weekend then the water supplier will be looking "very closely" at the need to introduce a hosepipe ban.
Reportedly, those who are found to be ignoring the ban could be charged a €125 fine.
Meanwhile, speaking earlier this week, ICMSA president Pat McCormack commented on the arrangement in place with Irish Water.
The forecaster added that the drought conditions are set to continue.
With no rainfall expected this week, the firm is encouraging its five million customers to use water more wisely in order to help ensure that the huge demand can continue to be met.
A similar ban is in place across Northern Ireland.
A hosepipe ban means that it is illegal to use a hose, whether it's from watering our gardens and washing cars to filling up paddling pools.
And the water utility firm is warning that it will take weeks and "even months" for water levels to restore in rivers, lakes and reservoirs. Use a watering can for your plants, and a bucket and sponge for your auto, and you'll be doing the environment a good turn. We have already seen some businesses committing to turn off their sprinklers and only washing the windscreens, mirrors, lights and number plates of their vehicle fleets, which is beneficial to the wider community.
Leakage Find and Fix crews are mobilised to reduce the water being lost through leaks both on the customer side and in the public network.
How can I reduce my water usage?
Irish Water has also appealed for the public to report leaks on the public water network and to fix private leaks in homes and businesses.