Police were pelted with petrol bombs and masonry during three hours of disorder on Friday.
The PSNI have said that 14 officers were injured in the violent scenes on Friday.
The disorder took place in the Atlantic Road area of Coleraine, Derry/Londonderry, where a crowd of about 40 people, many of them wearing masks, attempted to block the road by setting fire to pallets.
Police were also attacked with missiles and a car was set on fire in a separate incident at Tiger’s Bay, a loyalist area in north Belfast, where three teenagers were arrested.
Fourteen officers were injured in Friday’s unrest, bringing the total number of officers injured in the recent disorder to 88.
On Saturday two men charged with rioting offences in the Lanark Way area of west Belfast during the week were denied bail at Laganside Court.
North Area commander, Chief Superintendent Davy Beck, said: “The senseless disorder we saw unfold in a residential area in Coleraine has achieved nothing but leave people petrified in their homes.
“Such reckless criminal activity has only served to harm the local community by those who deliberately chose to engage in such disorder.”
The disorder in Coleraine started at about 7.45pm, when police officers had two petrol bombs thrown at them.
Five more petrol bombs were thrown when more resources were deployed into the area.
Masonry and other missiles were also thrown at officers, causing damage to some police vehicles.
At about 10.45pm, officers had dispersed the crowd and restored order.
Mr Beck added: “Thankfully, none of our officers were injured as a result of the attacks, however some of our vehicles did sustain damage, and that damage is currently being assessed.
“I want to make a direct appeal to parents, guardians and community leaders to use their influence to ensure we do not see a repeat of such ugly scenes.
“This is not wanted by anyone and does not represent the local community who we know just want to live in peace.
“I want to reassure the community that we will continue to work to keep people safe and those who engaged in last night’s disorder should be warned that an investigation is under way and evidence gathered will now be reviewed and those identified will face the full rigour of the law.”
Three teenagers, all aged 14, were arrested at Tiger’s Bay following the disorder on Friday and have been released pending further inquiries.
During the disorder, which started shortly after 5pm, petrol bombs and masonry, including roof tiles, were thrown at police.
There was an attempt to hijack vehicles on Limestone Road and, on North Queen Street, a car was hijacked and set on fire and pushed towards police lines.
Leaders in Northern Ireland are fearful the chaos that has plagued the region in recent days will continue into the weekend.
Loyalists have urged their communities to end any protests as a mark of respect for the Duke of Edinburgh, who died on Friday.
Despite this, small pockets of unrest continued in parts of the province.