Prime Minister Leo Varadkar said threats against politicians had increased recently and what happened outside Leinster House was inappropriate, reports RTE.
Following the incident on Wednesday afternoon, the MP and staff were unable to leave the premises of the National Parliament for several hours.
Ceann Comhairle Seán Ó Fearghail said a security review of Leinster House, involving gardaí and senior Oireachtas officials, would be “carefully considered”.
He spoke after a meeting with the Garda Assistant Commissioner and two senior officers, Dáil Clerk Peter Finnegan, Oireachtas Superintendent Barry Ryan and himself.
Ó Fearghaíl said the right to protracted protest is essential and must be protected.
The Ceann Comhairle said security issues were being “actively” considered in the Oireachtas and there would be “ongoing engagement” in the coming days before predicting a “set of proposals” would be put forward on how to deal with similar situations.
He said there was “every expectation” that incidents could be repeated in the future, adding that Gardaí had raised their concerns at the meeting and Oireachtas officers had shared them.
The Prime Minister said the right to peaceful protests was essential in a democracy, but what happened was not peaceful.
“What I saw happening outside Leinster House was not a peaceful protest. There was violence, there was intimidation and that was wrong,” according to Leo Varadkar, reports RTE.
Speaking at the National Plowing Championships in Co Laois, Martin said he believed those involved were “trying to create an alternative reality” aimed at undermining Irish democracy.
“Not only did they attempt to undermine the seat of Irish democracy in terms of the Parliament, the Dáil and the Seanad, they also upset and undermined people going about their daily business in Dublin, who are not at all impressed with the nature of the protests, if you could call them that. “I think some of these people are trying to create an alternative reality in terms of the country, undermining our democracy and some of it almost approximates to sort of fascist like behaviour in terms of intolerance,” reports RTE.
Justice Minister Helen McEntee said the “disgraceful” scenes outside the Dáil building had “no place in our democracy”, reports RTE.
“They do not represent the majority of people, and it cannot be the situation that something like this is allowed to happen or that it is allowed to continue in this way,” she said, reports RTE.
Speaking on RTÉ’s Morning Ireland, Mr Buttimer said: “I have never witnessed the behaviour and the thuggery of yesterday,” reports RTE.
The actions of Garda officers ensured that no one was seriously injured during the incident, he added.
In a statement, gardaí said a police operation had been carried out to facilitate the reopening of the 33rd Dail.
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