Allowing 50 person indoor gatherings is "certainly not intended to mean a house party", according to Dr Cillian De Gascun.
He also said a recent increase in new cases and clusters suggests "people aren't restricting their social network as we've asked them to do".
'Phase three' of the lifting of coronavirus restrictions began on Monday - allowing most businesses to reopen and many sports, social and cultural activities to resume.
However, people are still being asked to follow social distancing advice - with indoor gatherings restricted to 50 people, and outdoor ones limited to 200 people.
Dr De Gascun, the chair of the COVID-19 Expert Advisory Group and director of the National Virus Refence Laboratory, spoke to The Pat Kenny Show about the current coronavirus situation in Ireland.
He observed: "We're seeing an increased number of close contacts associated with the confirmed cases that we've seen in recent days.
"While that's to be expected as we reopen society, it also suggests that people aren't restricting their social network as we've asked them to do. We're not counting casual contacts in those numbers - we're just counting close contacts."
In terms of 50 person indoor gatherings, he said that means gatherings in locations where "social and physical distancing can be maintained".
He explained: "It's certainly not intended to mean a house party.
"It's intended towards locations like a church or town hall, where 50 people can be indoors but maintain physical distancing."
Ireland in a 'really good position'
Dr De Gascun said Ireland has for the most part done a very good job in controlling the virus.
He said the response hasn't been perfect, but we're now in a "really good position" compared to two or three months ago.
However, he warned it's important to not jeopardise that with travel abroad - warning that the "biggest risk" is importing cases from other countries.
In terms of the planned 'green list' of countries deemed safe to travel to, Dr De Gascun argued: "If we were to come up with a list or to have air bridges of a sort... it would obviously be limited to a small number of countries that would be in a very similar position to ourselves.
"The difficulty with that list is that it might change - I don't know what the frequency would be, but it might be weekly, might be fortnightly.
"To expect people to try and plan now for something in four weeks time based on a green list that might subsequently be out of date... We are asking people to stay at home for the summer, and support our own Irish tourism industry if we can."
He said he believes work is ongoing at Government level to ensure the advice to the public on travel is more straightforward.
In terms of face coverings, Dr De Gascun said he has heard feedback that the message to the public has not been 'consistent or convincing' - and acknowledged that authorities need to work on that.
However, he added: "There is also a behavioural element.
"People would have adapted to the physical distancing really well, very early on... the masks are something new for Irish people, that we haven't done before.
"People are very capable of doing it, but we do need to reinforce it."