An Garda Síochána say that they have recommenced Operation Fanacht - a plan to ensure public compliance with travel restrictions - as a localised policing operation in Kildare, Laois and Offaly.
The three counties were placed under local lockdown on Friday following a rise in confirmed coronavirus cases.
The new measures will remain in place for two weeks.
Legislation giving Gardaí the legal authority to enforce the movement restrictions was also signed into force yesterday.
Gardaí have said that they plan to police the restrictions in the same way as they did when the whole country was locked down earlier this year.
They say that there will be a high level of Garda visibility in Kildare, Laois, Offaly and in surrounding counties, and that checkpoints will continue to be established on relevant motorways and associated routes.
In a statement issued on Saturday afternoon, John Twomey, Deputy Commissioner of Policing and Security, said:
"Throughout the country, it is vital that people adhere to the public health regulations in an effort to reduce the spread of Covid-19.
"It is vital that we continue to work to minimise the risk to ourselves, our families and our local communities.
"We would appeal to all those living in these counties to stay and home and not undertake unnecessary journeys in an effort to reduce the spread of the virus."
Speaking on Midlands 103 today, Health Minister Stephen Donnelly urged communities in the affected counties to properly observe the restrictions:
"Why would anybody be saying to the guards, 'I am not going to do what the chief medical officer and the public health team are telling me'?
"Why would anyone have that conversation with the guards?"
Mr Stephen Donnelly also expressed his hopes that the measures introduced will help halt the spread of the virus beyond the clusters linked to meatpacking plants.
"Because of the extensive testing and tracing that has happened, it's been possible to act quickly, and the objective is to suppress the virus spreading quickly into the community," he said.
"The objective is to protect public health, protect vulnerable groups, protect the nursing homes, keep the reopening of the schools on track.
"Acting early also means that much less restrictive measures can be used than previous measures we’ve all lived through," he added.
Meanwhile, the Health Protection Surveillance Centre (HPSC) tonight reported that one patient diagnosed with Covid-19 has died, and that 174 new cases of the virus have been confirmed in Ireland.
112 of the new confirmed are associated with outbreaks or are close contacts of a confirmed case.
110 of the cases are located in Kildare.