Three men were detained by police yesterday as Orange Order chiefs pledged disciplinary action against members who attacked police lines at Drumcree.
The arrests brought to eight the number of men questioned in the aftermath of the latest outbreak of trouble which left 31 police officers injured.
A spokesman for the Police Service of Northern Ireland said he expected more arrests after Orangemen rioted when they were prevented from marching on the nationalist Garvaghy Road in Portadown on Sunday.
All the injured police officers taken to hospital after they were attacked with bricks and bottles have since been released.
Assistant Chief Constable Stephen White, the officer in charge of the security operation, said several troublemakers had yet to be questioned. But some of them had been identified.
He said: "There are a number of people who have been identified and there are others who will be identified. Members of the public have already called us to tell us who these people are. So, for those who engaged in violence right from the start there will be a price to pay."
The First Minister, Mr David Trimble, said after visiting an injured police officer in hospital, that it was "appalling that we have had so many police officers injured". He did not attach any blame for the disturbances on the organisers of the parade at Drumcree, the Portadown Orange Order District Lodge.
"But some people who thought they were coming to support Portadown district ended up doing an enormous amount of damage to Orangeism and to our hopes for a peaceful summer. Those Orangemen who engaged in an attack on the police let themselves down, let the institution down and I hope very much that the leadership of the Orange Order look at this very carefully to see what can be done."
Earlier three men appeared in Craigavon Court charged with riotous assembly. Mr David Cully (43), from Markethill, Co Armagh; Alan Cheney (17), of Glengormley, Co Antrim, and Mr Mark Wilson (37), of Maghera, Co Derry, were remanded in custody to July 25th.
The police decision to charge the men with the more serious scheduled (terrorist) offence of riotous assembly, as opposed to riotous behaviour, meant the court had no alternative but to remand them in custody. They are to apply for bail at the High Court in Belfast today.