HARDLINE republicans were behind the attempt to storm the Dail, resulting in violent attacks on gardai.
Leinster House went into lockdown last night as republicans and socialists attempted to storm the building.
Dozens of protesters led by dissident group Eirigi -- a breakaway faction from Sinn Fein -- and the Socialist Workers Party were fought back by baton-wielding gardai.
A further march is now being planned for next Tuesday sparking fears that more violence could develop.
In a notice to supporters today, the SWP website said the group "must escalate the action".
They accused gardai of acting in "the most brutal way" and said the attempted storming reflected "the spirit of Greek resistance".
Three people, including a pregnant woman, were killed during riots in Greece last week.
Senator Donie Cassidy, who observed last night's fracas from inside the main foyer of Leinster House, said a small group "put their heads down and tried to push through".
He told the Herald that gardai were left with no option but to draw their batons as they were "completely outnumbered".
A small number of protesters and gardai were injured during the Right to Work march which saw sticks and placards hurled at officers who formed a defence line across the Kildare Street entrance to the Dail.
The Herald understands that around 30 protesters carrying Eirigi and SWP flags broke away from the main march on Molesworth Street and arrived on Kildare Street via a side road.
The main protest organisers had cleared the event with gardai who were not expecting trouble, but sources say the peaceful protest was hijacked by a small element. Eirigi is a hard-line socialist republican movement formed in 2006.
Its main aim is to end British occupation in the north but it has also been central to protests such as that against the Corrib Gas Line in Mayo.
Colin Duffy, a man charged with the murders of sappers Mark Quinsy and Patrick Azimkar outside Massereene army barrack last year, is reported to have attended their protests in the past.
After his arrest for the murders, the group said he was no longer a member.
The scuffles lasted several minutes but today People Before Profit campaigner Richard Boyd Barrett claimed that gardai acted in a heavy-handed manner.
"Gardai overacted and immediately drew batons on protesters who attempted to walk through the gates.
"It was all over in a couple of minutes. I didn't see anybody running, they were walking. People attempted to walk through what was an open gate," he said.
But this description of events was disputed by Senator Cassidy who said: "They just thought they could bulldoze and walk through."
He said it would have been "an unprecedented breach of security" if the protesters had managed to break the Garda cordon".
At one point during its coverage of David Cameron's arrival in Downing Street, Sky News was also reporting that the Irish Parliament had been stormed.
However, a spokesperson for the House of the Oireachtas released a statement, saying: "A small number of protestors attempted to gain access to the confines of Leinster House, however, contrary to media reports they did not gain entry to the Parliament buildings or its grounds but were stopped by the Gardai."
Asked by the Herald if he condemned the hurling of objects towards gardai, Richard Boyd Barrett replied: "I don't think anything protesters did justified that [the gardai's response].
"People were just trying to make a peaceful protest. It's interesting that the media focus on incidents that are somewhat peripheral."
Another march by the Right to Work group is now being planned for next Tuesday evening, amid fears that it will lead to further violence.
Estimates for the number of people who attended last night vary between 500 and 2,000, but a notice on the SWP website today calls for greater numbers to join their crusade.
Mr Boyd Barrett said he has "no concerns at all" that the follow up march will cause more trouble.
"I think the politicians and particularly the Government are just not listening to what the public are feeling at the moment. They are protecting people responsible for the economic crisis and sacrificing the livelihoods of ordinary people," he said.
Senator Cassidy said he had no problem with people protesting peacefully.
"In the national interest everyone has to make sacrifices," he said.
Massive riots outside the Greek parliament last week led to the deaths of three people as protesters hurled Molotov cocktails at police and buildings.
An estimated 100,000 people took to the streets there during a nationwide wave of strikes against spending cuts aimed at saving the country from bankruptcy.