Drivers from Northern Ireland attempting to cross the border with the Republic are now being turned away unless they have essential reasons for travel.
Under new Covid-19 rules introduced on Monday, people trying to cross the frontier can face fines of up to €100 (£80), although police say penalties will only be handed out as a "last resort".
A number of Garda (Irish police) checkpoints are operational along the 310-mile long border, in a move aimed at discouraging travel and to reduce the spread of Covid-19.
The new measures apply to anyone who is "not ordinarily resident" in the Republic of Ireland, the police said.
One 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, said: "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.
"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, 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.
The Garda said, if enforcement is required, a fixed payment notice for €100 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.
Under Ireland's current Covid-19 public health restrictions, travel is restricted to within five kilometres (3 miles) 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 is advising against all non-essential travel.
Additional reporting by Press Association
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