The Health Minister Stephen Donnelly says pubs and restaurants need to 'do the right thing' around checking Digital COVID-19 Certificates.
It comes as a Department of Health survey suggests one in three premises are not checking that people are vaccinated.
Use of the certs was supposed to be scrapped this Friday, but this has now been extended until February next year.
Pub and restaurant opening hours are returning to normal from the end of this week.
But restrictions around mask wearing, social distancing and table service only - with limits of 10 people per table or 15 when children are involved - remain.
Minister Donnelly says hospitality businesses assured the public they would operate safely.
"We cannot just rely on the HSE or the HSA - the people running the pubs and restaurants, they need to do the right thing.
"Two-thirds of them are, one-third of them aren't.
"And that one-third really needs to step up now, and do the right thing as we come into winter".
Enforcement measures are being discussed at a meeting of the Government's Regulatory Forum - which includes Government officials, Gardaí and the Health and Safety Authority (HSA).
Earlier Social Democrats co-leader Roisin Shortall criticised the new easing of restrictions as having very few measures to help bring case numbers down.
She told Newstalk Breakfast while she welcomes plans to extend the Digital COVID Cert, the enforcement is not there.
"The Government's own data would show that about a third of the premises that were checked weren't bothering with COVID Certs.
"And that needs to be dealt with.
"At the moment there is a lack of clarity around what agency or who is actually responsible for enforcing that.
"There's a very small number of HSA inspectors - they've their own work to do, they don't work out of hours - so there needs to be a better enforcement mechanism," she said.
Additional reporting: Kacey O'Riordan