People are still behaving in a “reckless” manner and are not abiding with social distancing rules, Justice Minister Naomi Long has said.
Mrs Long said that, in general, people had been keeping to the rules better than last weekend.
But, she said, people were still travelling to areas like the beach to go for a walk.
New powers to enforce guidelines on staying at home and businesses staying closed have come into force in NI.
The regulations were published on Saturday.
They include the ability to force businesses to shut and crack down on people who leave their homes without a “reasonable excuse”, which includes:
- Obtaining basic necessities, including food and medical supplies
- Taking exercise either alone or with other members of your household
- Seeking medical assistance
- Providing care or assistance to a vulnerable person, or to provide emergency assistance
- Donating blood
- Travelling for the purposes of work or to provide voluntary or charitable services, where it is not reasonably possible for that person to work, or to provide those services, from the place where they are living
- Attending the funeral of a family member
Penalties, ranging from fixed penalty notices to fines of up to £5,000, are being introduced as enforcement.
The maximum fine will be reserved for businesses but people could face a maximum fine of £960 if they do not comply.
“Take your dog for a walk, but do it locally,” Mrs Long told BBC’s Good Morning Ulster programme on Monday.
She said she did not want to see people being fined.
“We aren’t trying to be killjoys,” she added.
Police Service of Northern Ireland Chief Constable Simon Byrne said that there were a few occasions over the weekend where people were travelling to Northern Ireland’s “beauty spots”.
Mr Byrne said that in one case police had to tell a person that was self-isolating to return home.
On Sunday, the chief constable said police will use the new laws to enforce coronavirus-related restrictions on public life only when “absolutely necessary”.
He said officers will issue a £60 penalty to those failing to comply with the measures if required.
Meanwhile, Mrs Long also said that more than 200 of the 1,000 prison officers in Northern Ireland are self-isolating.
This is an increase in the number of prison officers in isolation since last week.
Mr Byrne said there are two members of the policing staff confirmed to have Covid-19, but that the PSNI’s absence in work rate is one of the lowest in the policing force across the UK.
He added that the PSNI has “significantly stepped up” the amount of personal protective equipment it has for officers.
A flight from the Republic of Ireland to China to collect personal protective equipment (PPE) landed back in Dublin overnight.
It is the first of 10 flights to Beijing to deliver PPE to Ireland as part of a €208m (£180m) deal.
Some of the PPE from these flights is believed to be destined for Northern Ireland.