DUP representatives are set to meet the PSNI after a paramilitary-style parade involving up to 40 men and women wearing military clothing took place in west Belfast.
The march, organised by republican group Saoradh, was one of a number of dissident demonstrations that took place on Saturday.
Nine republicans were arrested after disturbances at the annual Easter Rising commemoration in Lurgan.
Two of those arrested have been released on bail while six men will appear at Lisburn Court today.
A 76-year-old woman was injured during the disturbances and was taken to hospital.
Police were present at the Unfinished Revolution march from Divis Street to Milltown Cemetery in the city.
However, they made no arrests despite dozens of participants wearing military fatigues, berets and sunglasses.
William Humphrey of the DUP said the PSNI and Parades Commission should be doing "all they can to prevent such scenes" from happening again.
The North Belfast MLA said: "There's no place for any such scenes in a civilised society in 2018 and whether it's Lurgan or west Belfast, it shouldn't be happening. The police and the Parades Commission should be doing all they can to prevent it from happening."
He said the DUP are now seeking to meet both the PSNI and Parades Commission over the parade in west Belfast.
He added: "We need an explanation as to why police didn't intervene. These scenes are not acceptable. We need to ascertain to why they had an operation in Lurgan but none in west Belfast and whether those parades that took place in west Belfast were illegal."
Police defended their operational response in Belfast saying it was "monitoring and gathering evidence".
Superintendent Robert Murdie said: "A specific policing plan was put in place for a parade by the National Republican Commemoration Committee from Divis Street to Milltown Cemetery.
"Our priorities were to keep communities safe, preserve public order, uphold the human rights of all and gather evidence of any wrongdoing. We took the decision to run an operational response that would focus on monitoring and gathering evidence of any offences.
"We will review that evidence and where we identify any individuals committing offences, we will seek to bring them to justice.
"I want to be clear that for anyone who engaged in actions that were unlawful, there will be consequences through the criminal justice system."
Following Saturday's parade in Lurgan, police charged five men aged 48, 39, 36 and two aged 30 with taking part in the illegal march.
Another man aged 28 has been charged with three counts of assault on police, taking part in an unnotified public procession and wearing clothing as a member or supporter of a proscribed organisation.
The six are due to appear at Lisburn Magistrates Court today.
A seventh man, aged 44, has been charged with two counts of obstructing police and assault on police.
He is due to appear at Craigavon Magistrates Court on Friday, April 27.
Two others were released on bail pending further police enquiries.
Ulster Unionist Doug Beattie was among those to praise the police operation in Lurgan.
Mr Beattie said: "Every year Republic Sinn Fein flout the law and organise an illegal terrorist show of strength in the Kilwilkie estate in Lurgan. Every year the PSNI have held back and adopted a low profile in an attempt to dissuade them from doing similar in the future.
"That was until March 31, 2018. On Saturday the PSNI said enough is enough and through a well co-ordinated plan delivered with professionalism and skill they broke up this illegal RSF gathering and arrested the colour party."
DUP Upper Bann MLA Carla Lockhart added: "I hear plenty of comments from republicans on legal Orange parades but they are strangely silent when republicans decide to march whenever they want glorifying terror in an illegal march.
"It is good to see a robust operation to prevent this illegality rather than a follow-up arrest operation some weeks later."
Meanwhile, police have issued a warning as tensions begin to rise ahead of a dissident republican parade in Derry today. The march, organised by the Derry 1916 Commemoration Committee, will take place in Creggan.