The Government and Retail Excellence have both appealed to shop owners to abide by the rules amid reports that some non-essential retailers are justifying opening by stocking small amounts of items classed as essential, while some essential retailers are continuing to sell items considered non-essential.
Duncan Graham, chief executive of Retail Excellence, said there should be a level playing field for all involved in the retail space while the country is under Level 5 restrictions.
"Our message to retailers is do the right thing," he said.
"Let's get through this together," he added.
The appeal comes amid reports that some shops have placed essential stock in areas of their stores where non-essential items are for sale.
Minister of State for Business, Employment and Retail, Damien English, stressed the importance of businesses working not only to the guidelines and regulations but to the spirit of those guidelines and regulations.
"Under the new rules, retailers with mixed retail offerings which have discrete spaces for essential and non-essential retail should make arrangements for the separation and closure of non-essential retail," he said.
"During this period of restrictions, I would ask all essential retailers who can remain open to be conscious of how your trade impacts on your colleagues who are closed or only operating a click and collect service."
Paul Allen runs the Allens chain of homeware and gift stores in Kilkenny, Athlone, Carlow and Limerick, all of which are closed today.
He said he had come across examples this morning where large essential retailers were selling non-essential items, contrary to the rules.
Under the Level 5 restrictions, retailers with a mixed retail offering which have discrete spaces for essential and non-essential retail, should make arrangements for the separation of relevant areas.
However, Mr Allen claimed that is not happening everywhere and that some stores were placing essential items in amongst non-essential ones so that those areas of the store could also remain open to shoppers.
He also claimed there was no enforcement of the rules taking place.
Mr Allen said that under the letter of the law, his stores could open, but he had chosen to close them in order to "do the right thing".
Many small retailers had just bought in Christmas stock, but are not able to sell it now as they have had to close down, he added.
But if other multiples are allowed to continue selling similar stock it will lead to a retail revolt, he claimed.
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Duncan Graham said it is not fair that small retailers that sell clothes or gifts for example should be closed if other retailers are still selling similar items.
He said if shops are doing things that will encourage shoppers to come into their stores, all that will achieve is the pushing back of the reopening date for everyone.
He also called for the Government to take a proactive role in enforcing the rules.
Last night the Tánaiste held a meeting with retail representatives and reiterated the Government's position around the issues.
In a tweet following the meeting, Leo Varadkar said he had taken the opportunity to "highlight the importance of everyone sticking to the spirit of guidelines to make this work."
"Essential retailers need to be fair to non-essential retailers," he said.
A spokesperson for the Tánaiste's department said today essential retailers were also reminded of the need to be fair to non-essential retailers, meaning that they should only sell items that fall within their remit as an essential retailer.
"The new regulations came into force at midnight last night and engagement with essential retailers is continuing in this regard," the spokesperson said.
Retailers were also asked to stagger opening times, to reduce pressure on public transport, they added.
"The major multiples have undertaken to comply with Level 5 requirements. This commitment is welcome and there will be ongoing engagement with them to ensure that it is fulfilled," the spokesperson said.