Footage which appears to show shots being fired over the coffin of a veteran republican is to be raised at the next meeting of the Policing Board.
The PSNI said it is conducting a “robust” investigation into the matter.
DUP MLA Joanne Bunting welcomed the police probe, and said “every effort” should be made to prevent similar scenes in the future.
“Displays like this cannot go unchallenged in a Belfast housing estate,” she said.
“It is unacceptable. This should not be normal. It should have no space to take place in our society. Terrorism should have no place on our streets.
“I will be raising this at the next Policing Board meeting. With the next meeting not scheduled until September, I will be exploring how this can be expedited.
“The Board should make a clear statement that they stand as one against paramilitary displays.”
The footage emerged after a funeral took place for Alex Murphy at St Peter’s Cathedral in west Belfast on Monday.
The 61-year-old received a life sentence for the IRA killing of two soldiers in Belfast in 1988.
His coffin, draped with an Irish tricolour, was flanked from Murphy’s Falls Road home by men wearing black berets and sunglasses, and paused at the Republican Garden of Remembrance.
On Monday evening, a video was posted on social media showing a masked man firing shots into the air over an open coffin.
Superintendent Lorraine Dobson said a “robust investigation” is under way to “establish the full circumstances surrounding this incident”.
“Bringing any weapons on to the streets, whether imitation or real, is a reckless act and one that serves no other purpose than to cause fear and intimidation and puts lives at risk,” she said.
“This was not a sign of respect.
“This was a criminal act with no regard for the wider wishes of law-abiding people, carried out by those who would seek to exploit and control the community through the fear of violence.
“The footage shows a man walking out of the front door of a house just yards away from where the shots were fired, while it also shows a young boy standing beside the coffin as the volley of shots was fired.
“Firing a gun, in such criminal circumstances, will always have the potential to put lives at risk and is simply unacceptable.
“I want to appeal to anyone with information to contact detectives at Musgrave Street on 101.”
Traditional Unionist Voice leader Jim Allister urged police to investigate the footage, and also queried whether officers were in the area during the funeral.
Ms Dobson said police were present during the funeral, adding: “An evidence-gathering operation was in place and any evidence of offences detected will be put before the Public Prosecution Service.”
There has been cross-community condemnation of the footage and images from the funeral.
Ms Bunting added: “The glorification of all terrorism is abhorrent. Setting aside the shots being fired, this man was convicted for one of the most horrific and cruel acts of murder to take place in the Troubles.
“The murder was played out on live television. It laid bare the hatred. To glorify the man who carried out this atrocity is sick and abhorrent. It only serves to confuse the next generation. Bombs in 2019 are wrong but so were bombs and murders in 1988.”
Ulster Unionist MLA Doug Beattie said such sights should have been left behind in the past.
“Such funerals and firing parties require a degree of organisation, not least in terms of the weaponry on display and how it is maintained and transported,” he said.
“This was an IRA funeral attended by well-known and senior republicans, and involved a group that was supposed to have decommissioned and disbanded.
“I understand the police have a very difficult job to do and do not envy them.
“There is also an onus on the Public Prosecution Service to explain the bar it sets for prosecuting cases involving paramilitary displays.
“As far as a reasonable bystander is concerned, anyone involved in yesterday’s event wearing berets, matching clothing and ‘D Company’ armbands was involved in an illegal paramilitary display and should be prosecuted accordingly.”
SDLP West Belfast representative Paul Doherty said there is no place on the streets of the city for masked men with guns.
“It doesn’t matter who is beneath the mask, what their motives are or where in the city it happens, there is no place on the streets of Belfast for masked men with guns to assert their influence or dominance in our communities,” he said.
“The practice of firing shots above coffins in residential communities has to stop. It’s dangerous, illegal and it’s clearly having an impact on community relations.”
Murphy was one of two men who received life sentences over the IRA killing in March 1988 of corporals David Howes, 23, and Derek Woods, 24.
In scenes that caused widespread shock, the two soldiers were dragged from their cars, stripped and beaten before being shot dead after they had driven into the path of a funeral for one of three people killed days earlier by Loyalist Michael Stone.