NI Water has said that demand for water is still 30% higher than usual due to the warm weather.
A hosepipe ban took effect in Northern Ireland at 18:00 BST on Friday.
On Sunday, the company said it was continuing to appeal for people to limit water use.
Customers in some areas, including parts of Lurgan and Coalisland, have already experienced loss of pressure and intermittent supply failures.
NI Water's CEO, Sara Venning, said while she was thankful to those customers who were abiding by the ban, demand remains "much higher than normal".