Petrol bombs and stones have been thrown close to the Ardoyne shops in north Belfast, the police have said.
Petrol bombs were thrown during trouble in Ardoyne
Dozens of officers are having to keep rival groups of nationalists and loyalists apart.
There is also a stand-off involving about 50 youths in the Short Strand area in the east of the city.
Earlier on Monday, a senior police officer said children as young as six have been involved in rioting in north Belfast.
District Commander Mike Little was speaking as he defended a charge that officers remained in their Land Rovers during weekend disturbances.
About 100 loyalist and nationalist youths clashed during rioting in the Ardoyne Road/Alliance Avenue area on Sunday night.
Missiles were thrown and windows in a number of homes were smashed.
Chief Supt Little said the first thing officers wanted to do was separate both sides.
Officers remained in their vehicles as he and senior officers spoke to community representatives in an attempt to calm the situation, he said.
Police action had to be proportionate to the situation and officers getting out of the Land Rovers could potentially escalate the problem, said the officer.
"I can assure the residents of north Belfast that we will continue to work to bring interface violence to an end. I am asking others with influence to do the same.
"Many of those involved in these disturbances are children, some as young as six years of age. This is a very difficult situation for police.
"These young people are causing disorder on the streets of north Belfast. I am asking parents and local communities to take responsibility for their young people. This is not a policing issue alone."
'Riot without consequences'
Sinn Fein councillor Margaret McLenaghan condemned those responsible for the violence.
Mrs McLenaghan said that whoever the perpetrators were, they were not representative of the Ardoyne community.
"What they are doing is wrong and they need to stop it because somebody is going to be killed here," she said.
Ulster Unionist Fred Cobain said the important issue was that rioters needed to be confronted by the police.
"People can't assume that they can riot without consequences - and that is what is happening at the moment.
"The operational decisions taken by the police, I think, are wrong - they need to be far more robust than they are."
Sunday's violence follows clashes between about 400 nationalists and loyalists during several hours of rioting in east Belfast the previous day.
One man was hurt and up to five shots were heard during those disturbances.