Mark Simpson said the clashes were across different parts of Belfast
One police officer has been injured and 15 people, including several children, have been arrested during loyalist protests in Northern Ireland.
There have been protests against restrictions on flying the union flag on Belfast City Hall, which the council voted through two weeks ago.
There were about 80 separate protests on Monday.
There was trouble in parts of Belfast, Lisburn, Carrickfergus and Portadown.
Police came under attack in Newtownards Road in east Belfast, where 200 loyalists congregated.
A PSNI officer was injured in Sandy Row, in the south of the city, when paint bombs, fireworks and bricks were thrown.
The latest trouble comes after more than two weeks of demonstrations by loyalists over the decision by Belfast City Council to stop flying the union flag every day. It will now be flown on up to 20 designated days a year.
Political leaders at Stormont have made repeated calls for the street protests to stop.
'Totally unacceptable'The PSNI said that numbers at the protests ranged from small groups to hundreds of people. They have appealed for an end to the violence.
Assistant Chief Constable Dave Jones said: "While most of the protests were peaceful, the violence witnessed in some areas tonight is totally unacceptable.
Analysis
What started as a political problem in Belfast quickly became a security headache and is now fast becoming an economic nightmare.
Two weeks of flag protests and roadblocks in the city have seen visitor and shopper numbers fall at what is supposed to be the busiest time of the year.
Some pubs estimate a 20% drop in festive business.
Christmas Day is only a week away but there is no end in sight to the flag protests.
It is not just a problem for the police and politicians but the economic well-being of the city - and its reputation.
"This is now the third week of protests and I am appealing to everyone involved to take a step back from this. It cannot and should not continue."
Police in Lisburn arrested five youths for public order offences, including an 11-year-old, a 12-year-old, two 13-year-olds and a 14-year-old.
In Portadown, a man was taken to hospital after being injured in a road accident during a protest.
In south Belfast, protesters set fire to bins and placed them across the Donegall Road near the City Hospital.
In Gaol Square, Armagh city, police arrested a 19-year-old man after a firework was thrown at police from a crowd of protesters.
Following a protest at Carrickfergus, about 11 miles from Belfast, protesters entered the town hall, disrupted a meeting and threatened councillors. No-one was injured.
Police dispersed the crowd and people were able to leave the building.
Alliance Party Councillor Noel Williams said that about five protesters were involved and described it as "a full frontal attack on democracy".
He said councillors were subjected to verbal abuse by the protesters who banged on desks and chairs.
"It is unacceptable that the town hall was not under police surveillance, especially as violence has broken out at previous protests," he said.
"People have a right to protest peacefully, but this incident tonight put many people's safety at risk and must not be tolerated."
In Lisburn, County Antrim, a crowd blocked Longstone Street. At Shaw's Bridge, in south Belfast, police diverted traffic as youths attempted to hijack vehicles.
Protests also took place in Londonderry and Ballyclare.
The protests, initially timed to coincide with Monday's rush hour, were also held in several areas of Belfast including the Albertbridge Road, Newtownards Road and Limestone Road.
Earlier on Monday, the leaders of the DUP and UUP, Peter Robinson and Mike Nesbitt, appealed to loyalists to call off the protests.
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