The protest action will be discussed during a special motion by cross-party politicians, who are under pressure to calm the situation.
Three 13-year-old boys were among several youths and men charged for taking part in weekend riots, which waned on Sunday. The Police Service of Northern Ireland (PSNI) said a number of protests over the flag controversy passed without incident.
More than 20 demonstrated at the bottom of the Shankill Road in Belfast while up to 300 people gathered on the Peace Bridge in Londonderry.
"Police have carried out evidence gathering in relation to the actions of some of these protesters and a file will be prepared for the Public Prosecutions Service," the PSNI added.
Nearly 2,000 people attended a demonstration at City Hall on Saturday.
Senior police had warned loyalist paramilitaries had been orchestrating some of the violence that has marred the city at the end of last week and appealed for calm.Political figures also called for an end to riots and disturbances.
The Northern Ireland Human Rights Commission condemned the action.
Professor Michael O'Flaherty, chief commissioner, said its first annual report was being published following a year in which the past has continued to haunt the present.
"Only last week we witnessed outrageous scenes of violence and intimidation when police, elected representatives and public servants were attacked," he said. "The recent murder of prison officer David Black also serves a reminder of how the most basic of human rights remain under attack in our society. We condemn these incidents, and all others like them, as attacks on us all."
Video: Protesters battle police in Shaftsbury Square on Friday