BELFAST, Northern Ireland (CNN) -- Loyalist paramilitaries are behind some of the violence seen in the past day in Northern Ireland, police said Saturday, as authorities appealed for calm ahead of more protests planned in Belfast.

Twelve people -- including a 13-year-old boy -- were arrested during disorder in the Belfast area overnight Friday into Saturday, the Police Service of Northern Ireland said.

Eight police officers were injured in the unrest, which followed days of violent outbreaks prompted by a decision Monday by Belfast city councilors to stop flying the Union flag year-round, restricting it instead to certain days.

"Police can now confirm loyalist paramilitaries are orchestrating some of the violence we have seen in the past 24 hours," Assistant Chief Constable Will Kerr said in a statement.

He appealed to anyone planning to protest in the city center Saturday to stay away and let people do their holiday shopping in peace.

"Violence has serious and unwanted consequences for us all, and we will robustly investigate all incidents," he said. "Today I am urging everyone to be calm, take a step back and think about how this violence is affecting not just their own communities but the whole of Northern Ireland."

About 1,000 pro-British loyalists joined a peaceful protest outside the city hall Saturday afternoon.

The latest disorder came hours after U.S. Secretary of State Hillary Clinton visited Belfast as she wrapped up a European tour.

Condemning the violence, she urged a continued commitment to peace during meetings with First Minister Peter Robinson and Deputy First Minister Martin McGuinness in Belfast on Friday.

"There can be no place in Northern Ireland for any violence; the remnants of the past must be quickly condemned," she said.

Clinton described the violence as "a sad reminder, unfortunately, that -- despite how hardy the peace has been -- there are still those who not only would test it, but try to destroy it."

Both Robinson and McGuinness condemned the violence and appealed for calm.

Four men were arrested Thursday after police investigating "ongoing dissident Republican activity" found what they described as a homemade rocket when they stopped a car in the area of Londonderry. An unexploded letter bomb was also found in a mail box, police said.

Buildings linked to the cross-community Alliance Party, which backed the Union flag's removal, have also been targeted. The party said Friday that its sole lawmaker in the UK parliament at Westminster, Naomi Long, had received a death threat.

The vote on the Union flag followed a summer of heightened tensions between Northern Ireland's Catholic and Protestant communities. Riots in September left dozens of police officers injured.

Just more than a month ago, a prison officer was killed in a suspected dissident IRA attack, the first such attack in years. In recent days, a number of suspected dissident IRA members have been arrested.

The recent disorder follows more than a decade during which Northern Ireland has made steady progress toward lasting peace and stability.

The majority of the island gained independence in 1921, following two years of conflict. But six of the nine counties of the province of Ulster chose to stay in the United Kingdom, eventually becoming the country of Northern Ireland.

In the late 1960s, the conflict between mainly Protestant unionists, who want Northern Ireland to remain part of the United Kingdom, and largely Roman Catholic nationalists, who want it to be reunited with the rest of Ireland, exploded into a political and sectarian war, known as the Troubles.

The three decades of ensuing violence between loyalists and the IRA claimed more than 3,000 lives, most of them north of the border. While the Good Friday Agreement of 1998 effectively ended the conflict, distrust remains between Catholics and Protestants.

Journalist Peter Taggart reported from Belfast, and CNN's Laura Smith-Spark wrote and reported from London.

™ & © 2012 Cable News Network, Inc., a Time Warner Company. All rights reserved.