The Government has warned it may use emergency legislation to shut down pubs that are still opening.
It comes after the Health (Preservation and Protection and other Emergency Measures in the Public Interest) Act was signed into law by President Michael D Higgins on Friday.
This gives the Minister for Health Simon Harris the power to prohibit and restrict certain events, and to close certain premises - for example pubs.
Speaking on Saturday as 102 new coronavirus cases were confirmed here, chief medical officer Dr Tony Holohan said: “The department is aware that pubs in some areas of the country are continuing to open, in contravention of existing public health advice.
"If any such premises become known to us, the minister will be advised to use his regulatory powers to enforce the temporary closure of premises in order to prevent the spread of COVID-19.
"We are also asking An Garda Síochana to assist in encouraging the public to abide by the public health advice on social distancing by encouraging any groups congregating in public to disperse."
All pubs around the country were asked to close by the Government to prevent the spread of the virus last Sunday.
However the request was not legally binding.
The Licenced Vintners Association (LVA) and the Vintners Federation of Ireland (VFI) both supported this decision, and urged all their members to close in line with the Government’s request.
The groups outlined "the real difficulty" in implementing the guidelines on social distancing in a public house setting, as "pubs are specifically designed to promote social interaction".
Justice Minister Charlie Flanagan said Garda patrols are being carried out to make sure pubs are staying shut.
"I spoke to senior Gardaí about that last evening and I do know that there have been checks - and that there will continue to be checks up and down the country."
He said this was to ensure "that the agreement that has been reached, between the vintners and the publicans on the one hand and the Government on the other, that pubs must close.
"We need to observe the social distancing".