The Welsh Government has said it will fully support police forces that choose to enforce tougher measures in response to people ignoring coronavirus restrictions.
Health minister Vaughan Gething added that he "cannot overstate" his "frustration" at those who have been caught flouting the rules.
It came as 1,898 new cases and 25 coronavirus-related deaths were reported in Wales, according to the latest data from Public Health Wales.
"The law is there in place for a reason, to keep all of us safe, and there are penalties for those people who break the rules," Mr Gething said.
"If the police take a more enforcement-heavy approach with people who are plainly doing the wrong thing and knowingly doing so, they will have the full support of Welsh Government ministers.
"All of us need to play our part and I cannot overstate my frustration with pictures of people who know they're doing the wrong thing, but are nevertheless doing so."
His comments came after a couple from Bristol were fined for travelling to the Gower Peninsula, Swansea, for a "holiday".The rule-breakers were caught in the Three Cliffs Bay area on Sunday, despite Wales being in alert level four, meaning only essential travel is allowed.A spokesperson for South Wales Police said: "Our officers are continuing to conduct random vehicle checks to ensure road users are only making essential journeys."Under Welsh Government level four restrictions, the advice is simple, stay home, If you blatantly breach them, you should expect to be fined."
Over the weekend, officers in north Wales also turned away visitors to Snowdon, with some travelling from as far as London and Milton Keynes - both of which are tier four areas.
Last week, South Wales Police revealed that officers responded to more than 200 reports of Covid breaches on New Year's Eve.
Gwent Police revealed that between 19 December and 4 January officers handed out nearly 60 fines.
The force said some of the excuses included visiting Wales to see the snow, going for a drive to Bristol following a self-isolation period, travelling to Walsall for a boxing session and attending a party.
Current restrictions have been in place since 20 December and are due to be reviewed on Thursday.However, Mr Gething was reluctant to specify when restrictions will be lifted during a Welsh Government briefing on Monday.
"There really is light at the end of the tunnel because we have two vaccines that are available," he said.
"We're seeing increasing numbers of those vaccines delivered over the coming weeks and months, more of us will be protected from harm, and that in itself is, in many ways, the biggest factor allowing more normality to return.
"When we get to Easter though of course, it's taking place in spring, and we know from the first period of time that as the weather starts to change, as it's more likely to be warm and dry, we're likely to have a different range of choices available to us.
"But I don't think we should set an artificial deadline within the period of the year when people can aim to do different things.
"It's really about us all pulling in the same direction, because the more we can do together, the quicker we'll get out of this, the quicker we will have some return to normality."Mr Drakeford also said there could be some tweaks "at the margins" but no significant changes because "it's difficult to see what more could be done".He also said the Welsh Government was unlikely to tighten restrictions despite the emergence of a new more contagious variant of the virus."We'll keep our plans under review but level four restrictions in Wales are very strict indeed and it's difficult to see what more could be done to them," he said."If they need to be tweaked at the margins to take account of the new variation that's what the cabinet here will consider."