The Executive has been urged to consider introducing a strict travel limit after more scenes of crowding at beauty spots here.
Police estimated that 1,000 people gathered at Crawfordsburn and Helen's Bay as temperatures soared on Monday.
It followed similar scenes at beaches over the weekend.
One MLA suggested a travel restriction should be imposed if the problem continues.
It came as Health Minister Robin Swann warned the battle against Covid-19 is "finely balanced".
Images showed crowds of mainly young people gathered at Helen's Bay and Crawfordsburn on Monday and not observing the two-metre social distancing guideline.
At the weekend parts of the north coast were packed, too, with reports that some people resorted to defecating in public as toilet facilities are currently closed.
Last Friday at Ballyholme beach in Bangor a police officer was injured while trying to disperse a large crowd of young people.
In a separate incident in north Belfast on Monday a 15-year-old girl required hospital treatment for a cut to her chest after being subjected to what the PSNI described as a vicious assault by a male gang after young people gathered at the Invest NI site near Springfield Road. A 16-year-old boy was also injured.
Northern Ireland's chief scientific adviser Ian Young said he fears the events of recent days could push the R-rate, the virus's reproductive number, above 1. Keeping it below 1 - it is currently between 0.8 and 1 - is crucial to avoid exponential growth in cases.
Alliance MLA Andrew Muir said that Stormont should consider toughening the restrictions, which currently permit travel to beauty spots.
"If this situation continues we're going to have to look at the regulations because we can't allow a repeat of that," he told the Belfast Telegraph.
"I know people have asked can police or Translink not turn people away, but the way the regulations are drafted there is unlimited travel, and also these locations are open.
"So whether we have to, unfortunately, close some of these beauty spots and beaches, which is disadvantaging the majority of people who are law-abiding, we have to do if there's a repeat of what happened."
Mr Swann, speaking at Tuesday's Covid-19 briefing, admitted that while the public's adherence to the lockdown was "fraying" he was not calling for police to be given additional powers to enforce the coronavirus regulations.
"I don't think we're in a place yet where we need further legislation to actually bring in further penalties on those young people who are gathering," he said.
"What I'm asking them to do is act responsibly, to think about their actions and the effect their actions have on their loved ones should Covid be found in their group of friends and the onward transmission that would have. In regards to empowering police to enforce a two-metre distance, I think that would put an enormous pressure on an already under-pressure police force at this minute in time."
At present the two-metre social distancing measure is a guideline, not a rule.
Mr Swann referred to images in the media in recent days showing long queues and crowds of young people at parks and beaches. He said that while he did not want to "lecture" young people, he urged them to show restraint.
"It does appear that for some people the compliance with restrictions and social distancing measures is starting to fray," he added.
"Our battle against Covid-19 is finely balanced. Yes, we have made important progress against it, we have flattened the curve and saved many lives.
"As a result of that immense effort we have started the process of cautiously and gradually edging out of lockdown.
"But we are still at a very early and tentative stage of that process. It wouldn't take that much to tip the reproductive spread of the virus over the all important '1' figure."
He reminded the public that this is not an "extended public holiday", adding: "People are staying or working from home for good medical and scientific reasons."
His comments were echoed by Infrastructure Minister Nichola Mallon and Justice Minister Naomi Long. They urged people to act responsibly to help defeat the virus.
"It is really worrying to learn of gatherings of young people on our rail services in recent days. The public health message is clear: social distancing must be practised by all individuals and each of us have a personal responsibility," said Ms Mallon.
Mrs Long said: "While there is no law against travelling to beauty spots to exercise and enjoy our magnificent scenery, I would urge anyone who does so to act responsibly when they get there."
Chief social worker Sean Holland said that while he backed Mr Swann's message to young people, some teenagers had found themselves in "difficult circumstances" during the lockdown.
"It is also worth remembering that some of those young people seen out and about in the parks have been in lockdown in situations that are far from ideal... some of those young people may have found themselves contained in homes in situations which are neglectful or abusive," he said.