Water supplies to around 700 households in the north west have been cut off because of burst pipes.
There are reports of pensioners without water for days, and businesses and restaurants have also been affected.
Northern Ireland Water said that an unprecedented number of leaks have been revealed during the thaw, causing "big pressure" on its systems.
However, the company said it had no plans to shut down any parts of the water supply in Londonderry.
"I know that some people would start filling baths and different utensils," their spokesperson, Paddy Cullen, said.
"It's totally counterproductive. If people start doing that it places further strain on a supply chain that's already at full capacity."
Moira Gormley, a 96-year-old blind woman, said she had been without water since before Christmas at her home outside Claudy.
She said she had been relying on friends and family to bring her supplies of bottled water for drinking.
"Things have been terrible here. The loos are a problem," she said.
"I'm terrified of using the water in the tanks because if it goes my heat will go too."
One restaurant in Derry, at Austin's Department Store, has been forced to shut by the crisis for the first time in 33 years.
"This was just the last thing we needed after such a rough December," Declan Hasson, from Austin's, said.
"People were desperate to get out of their homes now that the thaw has set in."