Health Minister Simon Harris has said those who are meeting other people from outside their household indoors are engaging in a "dangerous" activity.
It follows the first day of the easing of restrictions on Monday.
Outdoor workers - including constructions workers, landscapers and gardeners - returned to work with hardware stores, DIY shops and garden centres also re-opening their doors.
Car and bike repair shops also re-opened, alongside IT and phone shops, office suppliers, electrical stores and a number of others.
Minister Harris told Pat Kenny those arranging indoor meet ups with family and friends from other households risks delaying the re-opening of the country.
"At the moment, just to be very clear for all your listeners - and I'd appreciate if every family could have this conversation around the dinner table this evening: indoor gatherings with people from outside of your household is dangerous, it is not deemed to be safe, it is not allowed for currently and it could risk setting us backwards in relation to this pandemic".
He urged the public to adhere to the rules, and called on them to reflect on their good health.
"What I would say to anybody today who's finding this tough - and God I know it's tough too - we're all finding this tough, it's going on for a long period of time.
"What I would say to anyone is today, be thankful you're not one of the 55 people in intensive care today in an Irish hospital fighting for your life from COVID-19.
"Be thankful you're not the mom or the dad or the husband or the wife, or one of those people in one of those ICU beds".
"That is what we're trying to avoid here".
"This is actually the safest and fastest way of re-opening Ireland - if you actually try to do it quicker, all that you're going to do is spread this virus".
On the issue of making face masks compulsory for public transport, he said this will be kept under review.
"This is something we will keep under review, but at the moment the public health advice is that it's an additional hygiene measure that could have some benefit - but that it isn't mandatory at the moment".
He also said the Government is hoping to provide "more clarity" on gatherings, such as weddings, in the next couple of weeks.
Small gatherings are to be allowed under stage four of the re-opening, which is set for July 20th.
But he added: "Small is going to mean small: 100 is not small, 80 or 90 is not small.
"We're talking about a very, very small gathering with close family and very close friends".
"Nobody can guarantee where we're going to be in relation to this virus in the month of July or August".
He said the partial re-opening of the country is good news, mixed with a national nervousness.
"Early days yet, obviously - we've just seen I suppose one full day since we began the very gradual and slow easing of restrictions.
"But so far, so good seems to be my sense of it.
"I'm in the Department of Health here in the city centre and even as I look around the city centre and travel in from my own home and the likes whilst you notice some uptake in traffic, nothing too significant.
"And you do see people when they are out and about still adhering to social distancing."
"There is a reason we're going slow and steady at this plan.
"We genuinely believe the best chance we have of finding that - let's call it the sweet spot - where we can live alongside the virus and go about our lives in some normal way, is to do this in a slow and steady manner".
He said while everyone in the country can breathe a bit of a sigh of relief "that we're not in that terrible place we thought we could be", there is "a sense of national nervousness".
"If we get these next three weeks right, I'd really hope to be back on your programme talking about how we can now move forward and do more and travel and see more people.
"If we get them wrong, though... we could still see things go in the wrong direction".
"I don't want to be bringing a message of doom, but it is very fragile this progress".
