Matt Baggott, chief constable of the Police Service of Northern Ireland, said his officers will continue "to act as peacekeepers" but warned the region cannot afford a repeat of the violence. He added: "Others have a responsibility within the community and wider society to resolve the conflict and tensions surrounding parading."
Intensive behind-the-scenes contacts are underway in Belfast to try to prevent more rioting.
Political and community representatives are anxious to find agreement on arrangements for a major Orange Order march due to take place on September 30.
Among those involved in talks will be Northern Ireland's most senior politicians, unionist First Minister Peter Robinson and Deputy First Minister Martin McGuinness of Sinn Fein.
The violence, which came as hundreds of loyalists took to the streets in protest against a republican march, follows a dispute which first flared in July when a loyalist band stopped outside a Catholic church and played a contentious song.
Officers used water cannons on rioters who threw petrol bombs, bricks, bottles and fireworks at them on Monday. Some of those involved were seen breaking up masonry which was hurled at police. Police described the attacks on them as "savage."
Rioters damaged a nearby nursing home, vandalising equipment and setting bins on fire.
A spokesman for the home said: "None of our patients was hurt during the incident but this was a very distressing experience for this very vulnerable group of patients, many of whom have dementia conditions."
- Independent