Concerns have been expressed that such scenes were allowed to occur at the funeral of Real IRA leader Alan Ryan, despite up to 100 gardaí being drafted in for the service in Donaghmede.
According to An Garda Síochána, no arrests were made and enquiries are ongoing.
Justice Minister Alan Shatter said the scenes on Saturday morning were "reprehensible and absolutely unacceptable", but he added that he recognised the difficulties faced by gardaí.
Paramilitary trappings should not blind people to the fact that what is at issue is criminal terrorism.
Justice Minister Alan Shatter
"I recognise fully the immediate difficulties which face An Garda Síochána when people take advantage of a funeral to behave in this fashion," Mr Shatter said.
"But the Garda Commissioner has assured me that they are pursuing rigorously any breaches of the law which took place."
An examination of the scene by gardaí has taken place and an incident room has been established at Clontarf Garda Station.
"Gardaí, together with their colleagues in the North, will continue to take every action open to them to deal with the activities of members of these groups - whether they are engaging in terrorism or organised crime," Mr Shatter said.
Fianna Fáil has already called for action to address the public display of paramilitary activity.
"This was a full-scale paramilitary-style funeral in broad daylight in the middle of Dublin," Justice spokesman Niall Collins said.
"People are shocked and appalled by what happened and I am asking the Taoiseach and the Justice Minister to address this urgently."
"The scenes on the streets of Dublin yesterday were a stark reminder that attitudes and activity we thought we had left behind are still there in parts of our country.
"Every effort must be made to show these thugs that their criminal behaviour and their fear tactics will not be tolerated."
This sort of activity is not and never has been what Republicanism is all about. It is criminality plain and simple.
Niall Collins, Fianna Fáil
Alan Ryan was shot dead in Clongriffin, north Dublin, last Monday afternoon.
The convicted criminal, whose previous charges included taking part in a Real IRA training camp in Meath in 2001, had been due to stand trial accused of racketeering.
A man in his 40s was arrested on Wednesday night in connection with the Real IRA leader's murder.
But Ryan's killing sparked fears of revenge attacks and security was stepped up ahead of the 32-year-old's funeral at the Church of the Holy Trinity in Donaghmede on Saturday morning.
Adelina Campos from the Irish Daily Mirror told FM104 that the funeral was attended by about 500 high-ranking Real IRA members from both sides of the Irish border and at least 500 others.
"There would have been about 100 people who were in white shirts with a black armband, as well as seven people dressed in balaclavas and with sort of paramilitary uniform," she added.
"When they were out of the church, they changed in a white van. All the people in white shirts were around them, so no one could see what was happening, and then they dispersed in the crowd."
Earlier, at about 9.30am, a volley of shots was fired as Ryan's coffin was being removed from his house at Grange Abbey Drive.
Gardaí are appealing for anyone with information about the paramilitary activity to contact them at Clontarf Garda Station on 01-6664800, or via the Garda Confidential Line on 1800 666 111.