Supermarkets can use "discretion" over the Welsh Government's ban on selling non-essential items during the fire-break lockdown, the First Minister has said.
Mark Drakeford said people may need to buy such products "for entirely unexpected reasons which they couldn't have foreseen" during the 17-day period.
The restriction has seen aisles cordoned off and plastic sheeting placed over items including children's clothes, bedding and kettles.
Around 60,000 people have signed a petition submitted to the Welsh Parliament calling for the ban to be immediately reversed.
Under the fire-break 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, Mr 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.
He added: "They will want to do the right thing, I know, and our job is to be alongside them to make sure that is clear for everybody."
In an interview with BBC Wales, Mr Drakeford said Wales is in a "deeply serious" position and promised that any "anomalies" in the rules would be corrected.
"If the rules are not sensible rules, if there are anomalies that are emerging, we will put them right, but the basic underlying public health emergency has not gone away," Mr Drakeford said.
"The basic decision is the right one. If the implementation of it, the interpretation of it needs to be revisited to make sure the rules are sensible, then we will do that.
"Non-essential goods are not allowed to be sold over the next two weeks. That's why there are hundreds of shops the length and breadth of Wales are closed. The underlying issue is not about shopping, it is about saving lives."
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The ban on selling non-essential items was announced in the Senedd on Thursday after Conservative MS Russell George said it was "unfair" to force independent clothing and hardware retailers to shut while similar goods were on sale in major supermarkets.
On Sunday, the Welsh Retail Consortium called for the restriction to be "dropped quickly".
It warned that the "safe flow of customers" could be undermined due to changes in store layouts to cordon off areas.
Guidance previously published by the Welsh Government said certain sections of supermarkets must be "cordoned off or emptied, and closed to the public" during the two-week lockdown.