Watch: Video report by ITV Wales Work and Economy Correspondent, Carole Green
Revised guidance for retailers in Wales will be published on Tuesday after what the Welsh Government has described as "positive discussions" with the sector.
The Welsh Government said they were meeting with retailers on Monday to "review the regulations" on the sale of non-essential items in supermarkets to make sure the rules are being applied "fairly and consistently."
Speaking at a Welsh Government press conference, Health Minister Vaughan Gething acknowledged there had been confusion over the regulations.
Mr Gething said: "If there are anomalies we will look at whether the guidance needs to be revised and we will also strengthen it to make it clear supermarkets have discretion to sell to people who are in genuine need.
"We will take action today so that retailers understand that our rules already allow people in acute need to buy the basics."
Vaughan Gething said ministers would ensure retailers understand what can and cannot be sold during the 17-day firebreak, but also discuss how shoppers with "exceptional circumstances" can purchase non-essential items.
It came after Tesco was forced to apologise for wrongly suggesting sanitary products were "non-essential" and so could not be sold due to the new measures in place in Wales.
Mr Gething said the Welsh Government had been "listening carefully to what people have been saying" in regards to the restrictions.
He added when meeting with retailers on Monday, they would be discussing how shop staff would go about using their own discretion in a set of "limited circumstances".
The restrictions have seen aisles cordoned off and plastic sheeting placed over items including children's clothes, bedding and kettles.
More than 60,000 people have signed a petition submitted to the Welsh Parliament calling for the ban to be immediately reversed.
Several people ITV News spoke to in Rhyl said they thought the ban was "unfair". One supermarket worker said the rule can be frustrating and she just has to apologise to customers.
Under the firebreak lockdown, which began at 6pm on Friday and will end on November 9, non-essential retail including clothes shops, furniture stores and car dealerships must close.
Supermarkets have been told they must only sell essential items to discourage people from spending more time than necessary in shops and be fair to retailers who have to shut.
On Sunday Mark Drakeford told ITV Wales News: "I won't need - I don't think - to buy clothing over this two weeks and I think many, many people in Wales will be in that position too.
"For me, it won't be essential. But I recognise that there will be some people who for entirely unexpected reasons which they couldn't have foreseen will need to buy items.
"In those circumstances where those welfare reasons are at stake, we will make sure that our supermarkets understand they have the discretion to apply the rules differently."
Mr Drakeford said ministers would meet with supermarkets on Monday to discuss the ban.
Tesco was forced to apologise after mistakenly prevented customers from buying sanitary products.
The Health Minister said he was "saddened" by the incident. He said Tesco was "simply wrong" for not selling period products during the fire-break lockdown and confirmed they were essential items.
Mr Gething described the incident as "an incorrect reading of both the regulations and the guidance."
Tesco later explained that the aisle had been blocked off because of a break-in and not because they were deemed non-essential items.
Watch Monday's Welsh Government presser here: