Supermarket supplier Musgrave said it is experiencing high volumes of demand but its advice to the public is that there is no need for panic buying.
"Panic buying is an inconvenience to other customers, so we would reiterate the call to remain calm," said CEO Noel Keeley.
"We continue to work to maximise availability and are working with suppliers to keep products flowing through the system."
Mr Keeley said Musgrave is taking every step possible to ensure that the food supply chain continues to function as normal and the company is directly engaging with Government on the matter.
Retail Excellence also moved to reassure the public that shelves in supermarkets across the country will be restocked every evening and into the future.
The retail group spoke with all the major grocery multiples and forecourt operators today, and there will be a continuous supply to all grocery outlets for the coming months.
"We echo An Taoiseach's comments when this morning he confirmed that the shops will remain open and we have plans to ensure supply chains will not be interrupted,"said David Fitzsimons, group chief executive of Retail Excellence.
Mr Fitzsimons said there is no necessity to panic buy saying all major grocery outlets are "bulging with product".
He said the continuity of supply, especially in grocery, has been boosted by Brexit planning.
He said over the last few years all major groceries outlets had "doubled and trebled" warehouse capacity in planning for a potential hard Brexit and as a result are 'bulging with product'.
He said people "need to calm down" as robust contingency plans will ensure food supply "for months and months".
But he said we need to very carefully plan emergency supports for those businesses which will have to curtail hours or close.
Tesco said it recognises some products are currently in high demand and it is working around the clock with suppliers to restock stores every day.
"Our stores are open as normal and will continue to be. We ask our customers to keep shopping as they normally would," it said.
Lidl said that in recent days it had also experienced significantly stronger sales in many categories.
"Due to our robust and agile supply chain we are confident of maintaining supply of key lines as consumer demand remains high and our stores are continuing to receive deliveries as planned," it said.
But it also said it had put product quantity limitations in place on a select few product lines to ensure availability for as many customers as possible.
The company asked that customers respect these measures.
Tesco also confirmed that its home delivery service will continue to operate during the Covid-19 restrictions, and that it will top up state sick pay entitlements to ensure workers forced to self-isolate receive their normal wages.
A spokesperson said that they had a great cohort of drivers who were doing all they could to serve people.
In addition, Aldi says it will be limiting customer purchases to four units on certain lines from tomorrow.
It follows unprecedented demand across its range today.
Among the types of products where limits will apply will be tissues, antibacterial handwash, pasta and tinned tomatoes.
It says the move is to ensure all customers have an opportunity to purchase them.
Earlier, Lidl also said it had put product quantity limitations in place on a select few product lines to ensure availability for as many customers as possible.
The company said it was asking customers to respect the measures.
Both firms say they have comprehensive supply chain plans in place to minimise any disruption.