Gardaí adopted a "softly, softly" approach when dealing with breaches of the social distancing and travel restrictions over the Easter bank holiday weekend.
Final figures on the breaches will not be calculated and published until today but enforcement through arrests is said to have happened in only a "very small" number of cases.
Last night, it was reckoned the regulations, signed into law last week by Health Minister Simon Harris, were used by gardaí fewer than 20 times.
Officers said the public were largely compliant and accepted the advice of gardaí if they were found to be in breach.
Mr Harris last night said he believed the level of compliance among the public has been "very high" and that the types of instances of people gathering in large numbers, as happened in Glendalough recently, had not occurred.
Most of the offences recorded at the weekend were dealt with under the Public Order Act or road traffic legislation.
A handful of drivers were arrested for alleged drink- driving while a cyclist was stopped and questioned after he was found travelling on a motorway.
Gardaí in Limerick reported detecting a disqualified driver on a non-essential journey who had a child unrestrained in the back seat and seized the vehicle.
Elsewhere, gardaí at a Covid-19 checkpoint arrested a man for suspected drink-driving and also found what was believed to be cocaine in the vehicle.
"Many of the incidents that gardaí encountered involved stupidity and did not require the use of the temporary regulations," one officer said.
Another source said: "It has always been intended to use enforcement as a last resort. Enforcing these regulations through arrest has only happened a very small number of times."
The powers for gardaí, which can result on conviction in a heavy fine or a jail sentence for a serious offence, have now been extended until May 5. Many of the regulations cannot be deployed without the approval of the HSE, and this could prove to be a problem for gardaí if they want to implement them quickly in the coming days.
But that did not arise under the Garda's Operation Fanacht over the weekend.
The erection of 120 major checkpoints on main roads and another 500 on secondary roads on Thursday proved a big deterrent to motorists thinking of travelling to holiday homes.
A similar number of checks were carried out on Saturday and Sunday with around 2,500 gardaí deployed daily.
Public authorities also reacted quickly where there were reports of large crowds gathering for leisure activities and closed off access to many beaches and some parks.
A senior officer told the Irish Independent: "The softly, softly approach has worked out very well with the co-operation of the public and we want to thank them for that."
In the North, members of the PSNI had issued 107 fixed fines up to yesterday morning. These were mainly for refusing to disperse when asked by the police.
Officers said groups ranging from a dozen to 20 were found to have gathered for events such as house parties, barbecues and children's play dates.
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