Police in riot gear were involved in ugly clashes with Catholics who staged a sitdown protest on Belfast's Ormeau Road.
Each side blamed the other for causing the violence, while the Irish government later criticised the RUC.
There were other sporadic clashes between nationalist youths and police in Londonderry before and during the loyalist Apprentice Boys of Derry parades to mark the lifting of the siege of the city in 1689, the commemoration of which is one of the most important days of the Protestant marching season.
Nineteen police and a number of civilians were injured in clashes, though none of the injuries was reported to be serious.
The Irish government said it was disturbed by the violent scenes, junior minister Chris Flood saying he did not consider the RUC had exercised restraint in dealing with the Ormeau Road protest.
He added: "We have heard first-hand and very detailed reports and a local priest has expressed great anger to the Parades Commission. I am wondering whether it was right in this case to allow the parade to go ahead."
The priest, Father Anthony Curran, accused police of being heavy-handed. He also said he had approached the chairman of the Parades Commission, Alistair Graham, and told him he should be ashamed of himself for permitting the march.
Residents had erected a makeshift barricade of builders' materials across the Ormeau Road, then had sat down on the road.
When police in full riot gear moved in there were angry scenes as some protesters kicked and punched officers while policemen freely used their batons.
Residents' spokesman Gerard Rice claimed: "The police were brutal. It was the worst I've ever seen, but I'm relieved no one in my community is dead. I have never seen brutality like I saw from the RUC today."
But RUC Assistant Chief Constable Bill Stewart rejected the criticism as "outrageous", maintaining that a minimum amount of force had been used.
He added: "While many people did behave non-violently, others reacted with disgraceful violence in obstructing police officers charged with carrying out a legally binding ruling from the Parades Commission."
The Belfast parade, a small affair, took place without serious incident after the road had been cleared.
Its participants then made their way by coach to join 10,000 others in Londonderry for the main parade of the day.
In that city there were occasional clashes between police and nationalist youths, with a lorry set on fire and several petrol-bombs thrown.Reuse content