Businesses in the hospitality sector that do not enforce rules on Covid-19 vaccination passes "do not deserve to remain open", Minister Michael McGrath has said.
Stakeholders from the sector are set to meet Government officials on Tuesday to discuss compliance with the rules as well as risks associated with their wider reopening last month.
The Public Expenditure Minister has said outlets that do not enforce the rules are "putting everyone at risk".
Speaking on his way to Cabinet, he said: "Overall, we're seeing a pretty good level of compliance but we can do better.
"Any outlets that are not complying with rules are putting everyone at risk.
"And I think the public will increasingly vote with their feet and will leave the premises if they're not satisfied with the level of compliance."
Mr McGrath warned that there will be penalties for non-compliance.
"We do expect the minority of operators that aren't complying to fully comply with the rules. It's in all of our interests that they do.
"And if they don't, then there are penalties.
"The Government will act and the authorities will act and certainly any premises that does not comply with the rules does not deserve to remain open."
It comes after ESRI research found that the number of outlets not asking customers for Covid-19 certification had almost doubled in a month.
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The research, published last week, found that 37% of indoor diners in pubs said they were not asked for certification, compared with 21% the previous month.
For restaurants, 34% of diners said they were not asked for their Digital Covid Cert.
Taoiseach Micheal Martin said on Monday he wanted to see "maximum compliance" with the vaccine certificate requirement for indoor hospitality.
"The bottom line is, and the broader picture is that we want to see maximum compliance with existing guidance and existing regulations, particularly in terms of the vaccine certificate," Mr Martin said.
Monday saw 3,161 cases of Covid-19 had been notified in Ireland.
According to the latest figures, there are 498 patients who have tested positive for the virus in hospital, with 78 in intensive care.
