The acting Chief Medical Officer Dr Ronan says it is not inevitable that more counties will move to Level Three of coronavirus restrictions.
Dr Glynn is appealing to people in Dublin, Donegal, Louth, Kildare, Wicklow, Cork and Galway to pay particular attention to public health advice.
Stricter Level Three measures are now in place for Donegal and Dublin while spikes in the 14-day incidence rates of other counties are being closely monitored by the National Public Health Emergency Team (NPHET).
NPHET is also due to advise the Government as to whether cities, such as Cork and Galway, could be placed on higher Covid-19 restrictions instead of locking down entire counties.
Nuala O'Connor from the Irish College of GPs says people reducing their social contacts will make the biggest difference.
"What we need to do is we need to empower everybody to really understand that it really is the personal actions of each and every one of our citizens.
"Whether or not there are particular restrictions in place, it's how each and every one person chooses to act and chooses to spend their time- that's what is going to get us back in control of this virus."
On Friday 326 cases of Covid-19 were confirmed in the Republic, with no additional deaths recorded.
In a statement from NPHET, Dr Glynn said: “Today I am asking people everywhere but particularly in Donegal and Dublin to pay special attention to the public health advice.
“I ask every individual to take personal responsibility to prioritise who you need to see, limit the size of your social network and reduce your social contacts over the coming days and weeks.
“Because while there is every chance that other areas will have to move to Level Three, there is nothing inevitable about it. We have seen previously how people working together can turn the tide on this virus and bring increasing trajectories back under control.
“Know how valuable your individual actions are. Your choices and your actions are part of how we will succeed.”
