Gardai 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 that the regulations, signed into law last week by Health Minister Simon Harris, were used by the gardai fewer than 20 times.
Officers said that the public were largely compliant and accepted the advice of gardai if they were found to be in breach.
Mr Harris said he believed that the levels of compliance among the public had been "very high" and that the kind of instance of people gathering in large numbers, as happened in Glenadalough on a recent weekend, 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 drunk driving while a cyclist was stopped and questioned after he was found travelling on a motorway.
Gardai 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, gardai 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 gardai 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 the gardai, which can result in a heavy fine or a jail sentence for a serious offence, have 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 gardai if they want to implement them quickly.
But that did not arise under the Garda's Operation Fanacht - when more than 2,500 officers were deployed over the weekend.
A senior officer told the Herald: "The softly, softly approach worked out very well with the co-operation of the public and we want to thank them for that."
In the North, the PSNI had issued 107 fixed fines up to yesterday morning. These were mainly for refusing to disperse.
Officers said groups ranging from a dozen up to 20 had gathered for events such as house parties, barbecues and children's play dates.