Police vehicles were attacked with petrol bombs, hatchets and sledgehammers when they tried to disburse some 250 pro-British protesters in East Belfast, the site of the worst violence, CNN reported.
Three police officers were injured in the incident and six arrests were made.
Clashes were also reported between pro-British and pro-Irish groups in areas of Belfast where predominantly Protestant and Catholic communities meet.
Flying the British flag has long been a flashpoint between British loyalists who want to remain part of the United Kingdom and Irish nationalists who want Northern Ireland to join Ireland.
In December, the Belfast City Council voted to stop flying the Union Jack year-round and fly it only on certain days.
The chief constable for the Police Service of Northern Ireland revealed Monday that children as young as 10-and-11-years-old were involved in attacking police lines at the riots.
Chief Constable Matt Baggott blamed the continuing violence on members of the loyalist Ulster Volunteer Force.