Pressure is mounting for stronger legislation to enforce social distancing as a second person died in Northern Ireland after contracting Covid-19.
The patient was elderly, had an underlying medical condition and was being treated in hospital.
On Sunday night, the Department of Health said it would be writing to 40,000 people in Northern Ireland with underlying conditions.
In a statement, it said: "Those with underlying health conditions which put them at higher risk of severe illness if they contract coronavirus must stay at home to protect themselves.
"GPs will be writing to those in Northern Ireland most at risk (approx. 40,000) to provide them with more detailed advice."
Latest figures show 128 confirmed cases to date here, with 20 new cases announced on Sunday. However, concern is growing that lives are being put at risk because people are continuing to ignore the most basic advice.
Nutts Corner Market opened on Sunday, drawing widespread criticism, while young people continued to socialise at the weekend.
Health Minister Robin Swann has said that unless everyone follows the guidelines up to 15,000 people could die as a result of Covid-19.
It led to calls for the authorities to get tough on "selfish and reckless" behaviour.
Emergency legislation is set to be passed at Westminster on Monday which will grant the Government enhanced powers to enforce social distancing.
First Minister Arlene Foster said she "doesn't want to have to go down that road", but powers would be needed in some cases to prevent the spread of coronavirus.
"We're looking at where the risks are and how we managed those risks," she said.
"This is an emergency situation in Northern Ireland. Most people realise that is the case and we're taking the emergency steps that we need to take.
"Emergency legislation finishes its passage through the House of Parliament on Monday. There will be legislation which will allow us to enforce social distancing and all these matters.
"Of course, one doesn't want to have to go down that road but it appears that in some cases we are going to have to enforce it."
The plea came as the Department of Health announced a second elderly Covid-19 patient had died here.
Mr Swann said: "This heartbreaking news should bring it home to every one of us that coronavirus is a real and present danger across our community."
He said a minority of people continue to flout advice designed to minimise the coronavirus spread.
Mr Swann added: "These behaviours are putting the people themselves, their families and their friends and neighbours at risk."
SDLP MLA Patsy McGlone, a member of the Stormont Justice Committee, called for drastic measures.
"There are too many people out there who are simply not thinking. They are being reckless and selfish," he said.
"That's why I would have no hesitation in giving powers to police to crack down on those who are choosing to ignore the advice that is there to protect them.
"We may soon have no choice. It's approaching a time for drastic measures if people continue to ignore the warning we're seeing from countries like Italy."
Committee chairman Paul Givan MLA said every measure necessary is being considered.
"I will work closely with Justice Minister Naomi Long to ensure every law needed is in place to enforce the instructions being given to protect our community," he added.
Meanwhile, deputy First Minister Michelle O'Neill said all non-essential services should be shut down to prevent the spread of the virus.
She called on employers of all non-essential workers to allow staff to stay home and not to have them travelling and working.
"Anybody who's not on the front line providing food, providing pharmacy services, anybody who's not in that category, I believe you should be shut down," she said.
Primark became the latest big-name retailer to close its doors at the end of business on Sunday.
But across Northern Ireland many remain open and events have gone ahead, with many saying there is still confusion over what to do.
Appeals were made for people to stay away from Portrush and Portstewart, with images showing the beaches busy on Sunday.
Nutts Corner Market, which opened on Sunday morning, attracted strong criticism from politicians.
Reacting on social media, a spokesperson said: "According to government and council guidelines it was okay to open the outdoor market. If the market had been told to shut, we would have."
"Because it sells fruit and veg, meat, fish and poultry, food stuff that are in shortage in most shops, we trade no differently to a supermarket and we are probably a lot safer as we are in the open air."
Nutts Corner Market announced at 1.30pm on Sunday that it would be closing until further notice.