Large numbers of Garda checkpoints on main arterial and smaller roads have been set up across the country.
Gardai have been deployed at checkpoints nationwide to prevent people from travelling across the country for the May bank holiday weekend.
Operation Fanacht will see an extensive network of checkpoints established across the country.
Garda will also be patrolling tourists hotspots, major parks and walking routes in a bid to curb the spread of Covid-19.
#operationfanacht started today at 7am. Garda will be out on checkpoints and engaging with people all over the country, essential journeys in line with public health guidelines only. We can continue to #FlattenTheCurve#StayAtHome#WashYourHandshttps://t.co/SATjjbMGYs pic.twitter.com/sV5WgVQpVP— Garda Info (@gardainfo) April 28, 2020
The operation, which started at 7am on Tuesday, runs until the end of the May bank holiday weekend on Monday night.
It will involve checkpoints on many main routes, and thousands of mobile checkpoints on secondary routes and in towns and villages.
The operation will also see gardai conduct high-visibility patrols at major tourist locations, parks and beauty spots.
At any one time, there will be more than 2,500 gardai involved in checkpoints or high-visibility patrolling.
There will also be patrols near the border as previously seen around the Easter holidays.
Concerns have been raised about visitors from Northern Ireland travelling south of the border as the restrictions do not apply to people visiting the State.
Day-trippers from Northern Ireland cannot be arrested because of the legal loophole.
Deputy Garda Commissioner John Twomey said on Monday: “When we last ran Operation Fanacht there was a high level of compliance from the public. It is vital that we see that again.
“I want to thank the public for their co-operation so far. We know it has not been easy and has required significant sacrifices.
“We need this compliance to continue. This is a critical week for the country. If we all work together, we can help save the lives of our family, friends, neighbours and colleagues.”