Gardaí last week found 20 instances where the health regulations or licencing laws were potentially being breached by pubs.
Under Operation Navigation, gardaí have been carrying out checks on licenced premises to ensure that they are adhering to Covid-19 restrictions.
Under the current phase, only pubs that serve food are allowed to open, and patrons must show proof of having eaten a meal costing at least €9 if gardaí arrive for an inspection.
From Monday, 13 July, to Sunday, 19 July, gardaí said they found potential breaches of the regulations on 20 occasions.
"The majority of these cases continue to refer to no evidence of food being served or consumed and no evidence of receipts to show that food had been sold," said a garda statement.
Since the operation began on 3 July, gardaí have discovered 59 potential breaches, they said.
"In conducting these visits, An Garda Síochána continued its graduated policing response based on its tradition of policing by consent. This has seen gardaí engage, educate, encourage and, as a last resort, enforce."
When potential breaches of the public health regulations are found, gardaí are first requesting business owners to bring their businesses into compliance with the rules, before enforcement action is taken.
"Where potential breaches of the public health regulations are identified and where a person does not come into compliance with the regulations, a file is submitted to the Director of Public Prosecutions for a direction as to how to proceed," said gardaí.
They added that the vast majority of licensed premises are compliant with the measures.
John Twomey, Deputy Commissioner for Policing and Security, said that gardaí are continuing to see high levels of compliance with the rules and that "this is welcome".
The current measures for pubs will be in place until 10 August, after the last phase of reopening the country was postponed due to increased concerns about rising numbers of Covid-19 cases.
Gardaí said the pandemic "remains a real and present public health crisis", and appealed to customers and businesses to comply with the guidelines "in order to continue to save lives".