Gardaí say they issued more than 400 fines for non-essential travel since last Monday, 11 January.
More than 300 of these were issued at the weekend "for suspected breaches of the public health regulation relating to non-essential travel".
However, overall, gardaí said the vast majority of people were compliant with regulations this weekend.
They also reminded people that they cannot travel more than 5km to a location to exercise.
In Co Wicklow, 170 people were fined €100 each for travelling to the mountains, while another 30 in Co Longford were issued with fixed charge notices after they had travelled to Ballymahon where Newcastle Woods is located.
Gardaí say that despite widespread compliance with Level 5 restrictions, Wicklow was an exception, with cautions issued to more than 200 motorists and cars turned back on Saturday alone.
Gardaí at the checkpoint in Ballymahon said more than 70 drivers were asked to turn around and go home.
Roscommon / Longford Roads Policing undertook an operation at Newcastle Woods, Ballymahon today in support of the public health measures.— An Garda Síochána (@GardaTraffic) January 17, 2021
Approx 70 vehicles were turned around & over 30 fixed payment notices were issued to parked vehicles found outside their 5km #StaySafeStayHome pic.twitter.com/w4TjePLbTZ
Gardaí said while it is important for people to exercise and get fresh air, this must be done within a 5km radius of their homes in accordance with current Level 5 restrictions.
If public amenities are crowded, the public health advice is to avoid those areas.
Gardaí say motorists are at risk of having their car being towed away and impounded if they park illegally at such amenities, because it can hinder access by emergency services.
Under Level 5 restrictions, people are required to stay at home except for travel for work, education or other essential purposes, but can exercise within 5km of their home.
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Today Gardaí in the Wicklow Division issued over 70 Fixed Payment Notices and turned back over 200 vehicles after issuing a caution to the drivers.— An Garda Síochána (@GardaTraffic) January 17, 2021
The COVID-19 Pandemic remains a public health crisis.
A series of fines for breaches of Covid-19 guidelines came into effect on Sunday, 22 November but gardaí only had the power to refer people breaking those restrictions to the Director of Public Prosecutions.
However, since 11 January, gardaí have new enforcement powers. These include the right to fine people engaged in non-essential travel.
A person travelling without a reasonable excuse can be fined €100 while organising an unlawful social or recreational gathering at home has a €500 penalty.
Ignoring a request to wear a face covering carries a fine of €80.
A court summons may be issued if fines are not paid within 28 days.
Up to 1,600 gardaí absent for Covid-related reasons
Garda Commissioner Drew Harris told RTÉ News this evening that 1,500 to 1,600 members of the force are out on Covid-related illness.
This figure varies from day-to-day, he said, but added that he believed a corner has been turned and gardaí and civilian colleagues are returning to work.
The Association of Garda Sergeants and Inspectors said it had requested this information from management on Thursday to provide welfare supports to members affected, but was told it could not be provided.
"We are disappointed to see it revealed to the media first," said the AGSI.
General Secretary Antoinette Cunningham added: "We are extremely concerned and worried about the numbers of our members affected by Covid-19 and also their families who are also impacted; as there are no facilities for gardaí to isolate away from their homes.
"We will continue to advocate for priority vaccinations for gardaí after frontline health care workers and the vulnerable in our communities are prioritised.
"The public must have confidence in our interactions with them that we are not inadvertently spreading the virus and we will continue to carry out our duties as best we can in these challenging times for gardaí."
Additional reporting: Paul Reynolds