by Rebecca Black, PA
Northern Ireland's Justice Minister said she does not want to see people fined over disobeying social distancing rules, but added that police need sanctions.
Naomi Long said it appeared that more people complied with social distancing at the weekend, but cautioned against some exhibiting "reckless" behaviour.
PSNI Chief Constable Simon Byrne said that there were a few occasions over the weekend where people were travelling to beauty spots, revealing that in one case, police had to tell someone that was self-isolating to return home.
New regulations to enforce social distancing in the region include fines of up to £5,000 for those failing to follow laws aimed at preventing the spread of Covid-19.
The regulations, which came into force at 11pm on Saturday, flow from the emergency laws passed at Westminster earlier in the week.
They ban gatherings of more than two people.
Ms Long emphasised that the rules are to keep people safe.
"We don't want to be in a situation where anyone needs to be fined, where anyone needs to receive a penalty," she told BBC Radio Ulster.
"We want to see people try to work with us through this crisis so that we can actually keep people safe. We're not trying to be killjoys, we're not trying to make people's lives difficult, we're trying to keep people safe.
"We're asking people to co-operate but those who persistently refused to - sadly we have seen again even just over the weekend that some people are behaving in quite a reckless way - then there has to be some kind of penalty imposed to drive the point home."
Mr Byrne said so far people have been "largely responsible".
"We have had a few occasions over the weekend where we have stepped up patrols in some of our beauty spots where we have had to advise people to go home," he said.
"There's one incident where we had to tell somebody to go back into their home over self isolating ... but by in large I think people have been really responsible and co-operative.
"But it's early days and we will continue to keep a high visibility presence right across the country in the week ahead."
On Sunday it emerged that six further people with coronavirus have died in Northern Ireland, taking the death toll in the region to 21.
With 86 new cases of the infection reported, the number of confirmed cases of Covid-19 stands at 410.
Ms Long added: "I think in general it was much better than last weekend, I think there were a lot fewer people who were out and around, there were a lot less in terms of public gatherings.
"But there is still - and perhaps some of it is due to confusion - there were still quite a lot of people who were heading off to the beach thinking that, 'well, if I drive to the beach and walk my dog there, what's the difference?'
"Well, the difference is, if everyone does that, you end up not being able to maintain the social distancing, but you also put pressure on services in areas that are really not designed for that at a time when what we need is for resources to be focused on dealing with the pandemic.
"I think the message is slowly getting through, I think we need to make it much clearer to people.
"We're saying you can go for a walk, you can take your dog for a walk - we are talking about local, we're not talking about taking yourself off to the beach at the weekend."