Northern Ireland retailers, RTE reports, are urging shoppers not to stockpile after problems with supplies left many shelves empty.
Smaller retailers say they fear months of disruption because of confusion about arrangements for importing food products (into Northern Ports see related story) from Britain following Brexit.
Retail Northern Ireland CEO Glyn Roberts said consumers should shop normally and not hoard products.
Speaking on RTÉ's Morning Ireland, Mr Roberts acknowledged there were some delays on goods getting to the shelves and retailers were working to resolve the problems.
He said many of their members in wholesale have been preparing for some time for this scenario to make sure they are aware of all the challenges, but said the focus now needs to be put on the Great Britain suppliers.
"The big challenge is a lot of the GB-based suppliers, who have clearly not been ready for this, have not had the forms filled in, or aware of the new system", he said.
He added that it is vital the British government reinforces that message so the GB suppliers are complying with the new regulations "because ultimately we are trying to ensure that hardworking families in Northern Ireland have the full product range and are not paying more for their grocery bill.
Are NI supermarket issues really just Brexit 'teething troubles'? (click here)
The British government has set up a special team to work with supermarkets trading in Northern Ireland which are having difficulties with deliveries.
Among the stores affected are those owned by Tesco, which has reported disruption of some supplies to its stores in Ireland since 1 January when the post-Brexit trade deal with the EU came into force.
Tesco CEO Ken Murphy said short shelf-life ready meals were among the products affected in deliveries to outlets in the Republic and to Northern Ireland.
For more here on this story.