Gardaí will focus on compliance with public health guidelines surrounding public gatherings and restrictions on bars and restaurants.
Targeted checkpoints will be set up around the county and there will be a high level of visibility of Gardaí.
People in Donegal and Dublin are being asked not to leave the counties, while people from other areas are being asked to avoid the two counties under Level Three restrictions.
Gardaí from surrounding counties, particularly Leitrim and Sligo, will also be involved in the operation, targeting public spaces that may attract people hoping to avoid restrictions.
An Garda Síochána will work in conjunction with the Police Service of Northern Ireland (PSNI) as cross-border spread of the virus has been identified as an issue by public health experts.
Operation Navigation, focuses on compliance with public health regulations by licensed premises, will also continue nationwide.
Deputy Commissioner, John Twomey said, "We all have a role individually and collectively in protecting ourselves, our families, our communities and the most vulnerable.
“It is vital that we all play our part to help reduce the spread of Covid-19 by adhering to the public health regulations and guidelines.
"Local Gardaí continue to be available to support individuals and local communities, in particular the most vulnerable in our society during this time.
“If you are feeling isolated or need help with shopping, collecting your prescription or anything else similar, please contact your local Garda station”.
Deputy Commissioner Twomey added: "An Garda Síochána is fully aware of the impact increased restrictions may have on those who are subject to domestic abuse and do not feel safe in their homes.
“An Garda Síochána takes domestic abuse very seriously. If you are in danger call 999 at any time. If you feel you are not in immediate danger and you require advice and assistance, you can visit or call your local Garda Station and ask to speak with a Garda in private. If you know of someone who cannot speak for themselves, please contact your local Garda station.”