Shops and other retail outlets should not be expected to police the wearing of face masks, which will be difficult to impose "unless the Government makes it mandatory", according to the Retail Grocery Dairy and Allied Trades Association.
Yesterday, the Government announced that face coverings must now be worn in all shops, retail settings and shopping centres.
The Government said the strong advice is for people to start obeying the guidance immediately, but regulations will take some time to draft.
Regulations to enforce the compulsory wearing of face coverings on public transport came into effect this week.
Speaking on RTÉ's Today with Sarah McInerney, Tara Buckley of RGDATA said "back up" will be needed to support staff.
She said while a lot of their members are putting up signs to advise people to wear face coverings, the challenge now is how it is going to be policed.
"Supermarkets have already had to up their security ... we would not like the onus to be on the shop to police it."
Ms Buckley said customers should know there will be spot checks or spot fines if they are not wearing masks, so that the message gets home that this is mandatory.
Regarding compliance, she said, there will always be that 1% of the public that do not comply with rules.
She cited examples of situations where some retailers have experienced people spitting and fighting in resisting the protocols and measures, which led to staff calling gardaí.
In relation to face masks for the public, she said she does not think the onus should be on shops to provide them free to customers, saying it is up to the public to realise they need their own face mask.
She said RGDATA members do not have any problem with the latest advice coming from the medical experts.
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John Douglas of the Mandate Trade Union said it welcomes the call to wear face coverings as it is reassuring for both staff and customers.
However, he thinks that the level of fines and a possibility of jailing is "OTT".
"I think someone running to the shop for bottle of milk facing a €2,000 fine or a jail term is draconian."
He thinks 99% of customers understand why we the masks are being imposed.
Speaking on the same programme, Public Health Specialist and Professor at the Royal College of Surgeons in Ireland Ruairi Brugha said if we do not take the right actions right now, we risk facing a second wave of the virus.
"Evidence has grown about the benefit of masks to reduce the risks. We have also said it is a sign to people we are taking this virus seriously."
He said ensuring people wear masks in any indoor venue apart from their houses will be a signal to people we are entering a more dangerous stage than the last two months.
He said the R number could get rapidly out of control if people don't act cautiously and he said where people congregate in poorly ventilated areas, that can drive up the numbers.
Sinn Féin's David Cullinane has highlighted the deep frustrations that many businesses will feel regarding the delays to reopening until next month.
He said businesses will need to be supported and his party will publish proposals on supporting small and medium enterprises (SMEs).
Concern has also been expressed as to how the Government delivers its message that wearing masks is now mandatory in shops and indoor settings.
Labour's Duncan Smith has said the Government needs to communicate this rule effectively with guidelines and an information campaign to ensure there is compliance.
Retail Ireland, the Ibec group that represents the retail sector, today said the health and safety of customers and staff is paramount and retailers will continue to follow the direction of Government when it comes to the use of face coverings in shops.
Retail Ireland Director Arnold Dillon said while business fully appreciates the important health considerations involved, there are also very significant staffing issues that arise, which need to be reflected in any new approach.
"When it comes to enforcement, it is crucial that it does not fall to retail staff to ensure compliance. With incidents of violence and abuse directed at retail staff unfortunately a regular occurrence, it is important that enforcement is left to the appropriate authorities. Retail staff should not be exposed to the potential disputes and discord that might arise," she said.