Taoiseach Leo Varadkar has described the actions of dissident group Saoradh, who marched in Dublin over the weekend, as "beneath contempt".
In a strongly worded statement last night, he said that: "People north and south are mourning the death of a brave campaigner and journalist Lyra McKee."
He pointed out that yesterday, the heroes of 1916 "who put Ireland on the path to democracy" were remembered.
Mr Varadkar had earlier attended the annual ceremony at the GPO on O'Connell Street to mark the Easter Rising.
"Others like Saoradh want to return Ireland to a violent and troubled past. We can never allow this to happen.
"Saoradh should apologise for their actions this weekend," he said.
There has been widespread condemnation of the decision by the republican group to parade outside the GPO on Saturday, within 48 hours of the murder of Ms McKee.
Mr Varadkar said that: "The right to assemble and march was won by the men and women of 1916 who fought for freedom and democracy we have today. This weekend they dishonoured their legacy and memory. It was an insult to the Irish people."
He said that listening to the proclamation outside the GPO yesterday morning, some of the words had resonated with him.
"The proclamation condemns those who in the name of Ireland would dishonour the flag through cowardice or inhumanity. Those involved in dissident activity should reflect on those words," he said.
Meanwhile, it took just 37 minutes to commemorate 103 years of our nation's "frail heart" at the annual Easter Rising ceremony yesterday.
Defence Forces chaplain Fr Seamus Madigan gave thanks for the dreams, wisdom and bravery of the 1916 leaders.
He asked that we look "beyond borders" and listen to the "voices that challenge".
Health Minister Simon Harris, Defence Minister Paul Kehoe and Higher Education Minister Mary Mitchell O'Connor and former president Mary McAleese were in attendance.
President Michael D Higgins also arrived to inspect the Guard of Honour.