Fines for non-essential travel were introduced two weeks ago and in that time An Garda Síochána has issued 1,500 such fines.
Deputy Commissioner John Twomey said it is unfortunate that there are still some people putting themselves, their loved ones and everyone they come into contact with at risk of getting Covid-19.
"There are people dying and are seriously ill from Covid-19. Our health service and all who work in it are under serious pressure.
"People need to adhere to the public health regulations to help save lives and reduce that pressure."
At close of business on January 24, 909 fines for non-essential travel had been processed.
In addition to these, there are approximately 645 fines are currently being processed.
Gardaí are reminding people that they are only allowed to exercise within 5km of their home.
The 5km limit includes the distance travelled from a person's home to a location for exercise. You cannot travel more than 5lm to a location to exercise.
An Garda Síochána is continuing its checkpoints and high visibility patrols at public amenties around the country.
If a driver is found to be in breach of the non-essential travel regulations, not only can the driver be fined but their adult passengers too.
This is also the case for adults in groups undertaking activities such as cycling and walking.
Gardaí are reminding the public that travel to airports and ports should only be taken for essential reasons. Holidays abroad are not considered to be essential.
Deputy Commissioner Twomey said: "Please keep yourself and others safe by staying home. Only make essential journeys. Limit your contacts. Practice social distancing. Wash your hands."