Holiday home and caravan owners who normally spend Easter in County Donegal have been told to stay at home.
Pleas have been made on both sides of the Irish border asking people not to travel.
It comes as An Garda Síochána (Irish police force) launched a major crackdown on the movement of people over the Easter weekend
There are about 10,000 holiday homes in Donegal, many owned by people from Northern Ireland.
Many of Donegal’s caravan parks have closed as part of current restrictions on public life in the Republic of Ireland.
Mayor of Derry and Strabane Michaela Boyle said anyone who is thinking of travelling across the border for the weekend should think again.
“Normally at this time people would be getting ready to move the family across the border,” she said.
“But these are extraordinary times and we are currently experiencing the most lethal public health emergency of our lifetime.”
Ms Boyle said how people act “will have a direct bearing on whether members of our families, of our communities will live or die.”
She added: “People need to act responsibly and make the right decisions over the next couple of days.”
The mayor said it should not surprise anyone to see an increase of police checkpoints in the coming days.
Gardaí (Irish police) have been granted new powers to enforce restrictions on movement over Easter and Commissioner Drew Harris said people should not be travelling to holiday homes.
A Garda (Irish police) spokesperson said: "We will liaise with our colleagues in the PSNI to deal with any issues that arise around cross border traffic, and would appeal to the public in Northern Ireland to fully comply with the regulations announced today.
Officers will be able to will be able to knock on the doors of holiday homes and caravans and instruct people to go home under new regulations signed into force on Tuesday.
About 50 checkpoints will be set up on roads to discourage people from travelling.
Penalties for those not complying include a six month prison sentence and fines up to €2,500 (£2,200).
'Do what is asked'
Independent Donegal councillor Micheál Cholm Mac Giolla Easbuig told BBC Radio Foyle’s Mark Patterson Show he was aware people have already travelled to holiday homes.
“That is not acceptable,” he said
“Right now we have to abide by what is being asked of us.
“Please don’t come to your second home. We want you to come when it is over and we will open our arms to you, but right now people need to stay in their own homes.”T
Towards the end of March, people were urged to stay in their homes until 12 April unless they needed to buy food, medicine or attend medical appointments.
They were told they could go out for exercise, along as they stayed within 2km (1.2 miles) of their home.
Exceptions have been made for a list of essential workers and those provide care for vulnerable people.
On Tuesday Health Minister Simon Harris signed regulations which will enable officers to enforce the rules.