The parade down O’Connell Street this weekend by republican group Saoradh dishonored the Irish flag, Taoiseach Leo Varadkar has said.
In his first comments on the event he said people North and South are mourning the death of murdered journalists Lyra McKee.
“On Sunday we marked the heroes of 1916 who put Ireland on the path to democracy. Others like Saoradh want to return Ireland to a violent and troubled past,” Mr Varadkar said.
“We can never allow this to happen. Saoradh should apologise for their actions this weekend. The right to assemble and march was won by the men and women of 1916 who fought for freedom and the democracy we have today.
“This weekend they dishonored their legacy and memory. It was an insult to the Irish people.”
The Taoiseach pointed to the words of the 1916 Proclamation which were read out on the steps of the GPO today as part of the official State commemorations of the Easter Rising
“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
While describing the demonstration as "very disturbing", he said Gardaí policed the event "appropriate and with restraint in the circumstances".
Meanwhile, Justice Minister Charlie Flanagan has defended Gardaí’s decision to allow dissident republican group Saoradh march down O’Connell Street in Dublin.
Around 150 people including two marching bands and a colour party dressed in military garb with berets and sunglasses took part in the parade on Saturday.
There was no effort on the part of Garda to stop the march despite its clear paramilitary tone.
In a statement today, Mr Flanagan said: "I know that all right-thinking members of the public are sickened at the sight of a small number of people in paramilitary uniforms, particularly after the horrific killing of a young journalist, Lyra McKee, in Derry on Thursday night.
"These demonstrators do not represent the views of the Irish people who have been united for many decades in rejecting paramilitarism and are rightly revulsed at this display."
But he added that Gardaí had to use "their training and judgment to balance the rights of people to demonstrate".
"They do this well and maintain the public’s trust. At the same time, I am regularly briefed on these matters and I am satisfied that the Gardaí prioritise the security of the state in monitoring of all dissident activity and will continue to do so, in conjunction with the PSNI and other security partners," the minister said.
The political republican group issued a statement absolving the "IRA volunteer" who shot Lyra McKee.
Saoradh's chairman and spokesperson, Brian Kenna, hit out at the "irresponsible PSNI who went into a nationalist area on Thursday night and provoked a young community".
Fine Gael senator Neale Richmond said Saoradh had "no place on the streets of the capital".
Last night police in Belfast were continuing to question two suspected teenage members of the New IRA about the murder of the 29-year-old journalist in Derry.
The men, aged 18 and 19, were arrested in Derry under anti-terrorism legislation and were brought to a police station in Belfast, the PSNI said.
Detective Superintendent Jason Murphy, who is leading the inquiry, said he believed both men were involved in the shooting. "Clearly my consideration is whether those two individuals acted in isolation or in collusion with other individuals, and I am keen for the community to come forward and help me answer that question," he added.
Ms McKee was killed in the Creggan estate in Derry after she was shot in the head by a gunman who fired toward police as rioting raged. Mobile phone and CCTV images captured chilling footage of a masked man pointing a handgun in the direction of police, close to where Ms McKee was standing among a crowd of bystanders.
Her partner, Sara Canning, led tributes to the investigative journalist, published author and LGBTQIA activist, saying her "amazing potential was snuffed out by this single barbaric act".
Det-Supt Murphy added: "People saw the gunman and people saw those who goaded young people out on to the streets, people know who they are.
"What we are seeing is a new breed of terrorist coming through the ranks and that for me is a very worrying situation."
He said Ms McKee's murder had created "a sea change" in the community and asked people to have confidence to come forward with information.
He added that the individuals responsible for her murder continued to "hide in the shadows" but his officers had identified "palpable" change in support of the police.
"This will be Lyra's legacy. Lyra's murder was not just an attack on Lyra, it was an attack on the fabric of this community. Lyra's killers have succeeded in only one thing, and that is in uniting the entire community in condemnation," he said.
A statement on Saoradh's website last Friday said a "republican volunteer attempted to defend people" from the PSNI and the RUC and that "tragically a young journalist, Lyra McKee, was killed accidentally".
Despite releasing a statement, Saoradh chairman Mr Kenna, who is a former employee of the HSE, told the Sunday Independent he had no knowledge about the shooting. He said the information was "passed" to Saoradh. "We would act responsibly in passing on information from republican sources," he said, while adding that he had "no information" to pass to gardai.
Saoradh secretary Ger Devereux said he did not see the statement before it went out. "I don't necessarily agree with it," he said. "But I can state quite categorically to you that we had no involvement in that [shooting]."
Both men said they were shocked by the shooting.