People travelling from Northern Ireland into the Republic are being turned back at the border if they do not have an essential reason for travel.
A number of Garda checkpoints were operating along the border on Monday to enforce the new Covid-19 regulations.
People living in Northern Ireland who cross the Irish border without a reasonable excuse face a 100 euro fine.
One such checkpoint, near Emyvale on the Tyrone-Monaghan border, had seen three motorists turned back on Monday morning.
Inspector Adrian Durcan from the Monaghan Garda Station told the PA News Agency: “We have a checkpoint which is here to enforce the regulations which are currently in existence, to ensure that people comply with the Covid rules.
“From 7 o’clock this morning, we’re here to advise people that anybody who is not ordinarily resident in this state, they are now liable to a fine of 100 euros, if they are travelling without an essential reason to be here.”
Inspector Durcan said no fines have been issued so far, but that some people have been turned back.
He said: “We have engaged with a few people who have not had essential reasons and on the advice of the guards, they have turned back.
“People have turned back when requested. I think it was three so far this morning.”
He said Gardai would issue fines to those not complying with the regulations and follow up through court summons.
“They will receive the fine and have 28 days to pay the fine. Failure to pay that fine will result in a court appearance,” he said.
“If they don’t pay it we will issue a summons in respect of the offence and we will follow through on that summons.
“We would have no concerns at the minute other than to ensure that people have an essential reason to travel.
“We’re here to encourage them and to explain to them that unless they are essential reasons we will be issuing fines.”
He added: “At the minute we have had excellent compliance from the majority of people and we thank them for that.
“But there’s still a minority of people who are not complying with the regulations and we’re here to ensure that these breaches aren’t reoccurring.”
The new measures apply to anyone who is “not ordinarily resident” in the Republic of Ireland.
The Garda said, if enforcement is required, a fixed payment notice for 100 euro will be issued to each person who is in breach of the regulation.
If Gardai stop a car with a driver and two passengers, then each of the three adults will receive a fine of 100 euro.
The new rules mean the Garda can turn back day trippers from Northern Ireland who cross the border.
Under Ireland’s current Covid-19 public health restrictions, travel is restricted to within five kilometres of a person’s home except for essential reasons.
Around 4,600 people have been fined for breaching Covid-19 regulations in Ireland.
About 3,500 of the fines were for non-essential travel, including around 375 for non-essential journeys to airports/ports.
People travelling to an airport or port to take a holiday abroad are liable for a 500 euro fine for undertaking a non-essential journey.
The Irish Government has advised against all non-essential travel.