An Taoiseach, Michael Martin is now out of the country at an EU Council meeting and is not due back until later this evening.
"We need to move up the levels as set out in the plan".
NPHET's daily statement says that the Health Protection Surveillance Centre (HSPC) has today been notified of three additional deaths related to COVID-19.
"Level 5, or Level 6, or Level 7 - it doesn't matter what level we go to unless we all act responsibly in this", he said.
"The basics are the basics - mask-wearing, washing hands, keeping distance - but particularly at the moment visitors to homes, except where someone needs [to], there's an essential reason to visit a home".
Minister Byrne said Ireland is already ahead of most other European countries with restrictions.
"So there's certainly an argument for what my colleagues are saying - a very good argument - but I think the medical advice needs to be looked at as well". He said he did not want to be rushed into making a decision on a Covid-19 lockdown until it was completely necessary to do so.
That would indicate a cabinet decision on the issue on either Monday or Tuesday.
"But at the moment, the restrictions are pretty strict".
"The higher the community transmission the more hard it is to protect medically vulnerable people in all heathcare settings".
"The restrictions at the moment are pretty strict".
According to RTÉ, the NPHET letter does not recommend the closure of schools and the government would consider tweaking a restriction on people not being able to travel more than five kilometres from their own homes.
"The situation is very serious and we will need further action in relation to this". He said that the Government would be "examining all aspects of this, and make sure when we respond, it will be with a comprehensive response".
The proposals are only being considered by the Government for the moment, and it's thought that they'd only be put in place should the Covid-19 situation in the country worsen considerably over the coming weeks.
Cavan, Monaghan, and Donegal are now under level 4 restrictions, meaning shops that sell non-essential items are not allowed to open for four weeks.