Cottonsoft is one of the country's largest makers and distributors of tissue products such as the CottonSoft, KiwiSoft and Paseo ranges of toilet paper and the Tuffy Kitchen Towel.
Country manager Kim Calvert said the company was trying to manage the situation.
''The recent unprecedented panic buying of toilet paper has resulted in many retailers seeing empty shelves, resulting in many households being deprived of the ability to purchase essential household commodities ... Toilet paper seems to have borne the brunt of this impact.
"Cottonsoft has a strong and robust supply chain with no raw material supply issues, however, the exceptional spike in consumer demand has led the company to introduce prudent measures to ensure product is replenished and supplies protected."
Some of the measures include restricting the range of products being made, extending factory hours and overseeing orders to check product was shared over the market.
In 2017, the company's Dunedin factory, in Timaru St, increased its staff to 21 and hours of operation from 76 to 120 per week.
At that point it was making 200,000 toilet rolls a day.
The company will also extend warehouse hours to ensure logistics run smoothly.
"Cottonsoft is working very closely with our trading partners to ensure continuous availability across the market," he said.
"Cottonsoft are monitoring supply, manufacturing and shipment of all products daily, and support retailer positions that panic buying is unnecessary, and that supplies of tissue products will remain available through the retail supply chain for households to purchase."
Prime Minister Jacinda Ardern has previously warned the public against panic buying, telling people to continue with everyday life.
"If you need a bottle of milk, go and get it. If you don't, do not react in any other way than you would any other day," she said a day after the first confirmed coronavirus case in New Zealand.
"The public should be going about their daily lives."