Security alerts in Londonderry and Belfast closed a school and a medical centre yesterday.
In the morning, St Columb's College in Derry was evacuated following the discovery of a suspicious object at a gate at a rear entrance to the school used by pupils.
It was later declared to be an "elaborate hoax" while a firearm and ammunition were found in the security alert in north Belfast.
In Derry, residents were also evacuated a number of homes and Templemore Sports Complex was opened as a rest centre.
Inspector Vince Redmond said: "I understand the disruption this incident caused for local residents who had to leave their homes as our officers worked to make the area safe.
"I want to thank the local community for their understanding and patience. Those involved showed a complete disregard to public safety and the education and welfare of those pupils impacted."
Sinn Fein MLA Karen Mullan condemned the alert, which caused "major disruption".
"This is disgraceful and the last thing that pupils, teachers and parents need this morning, particularly as children return to the first day back after the break," she said.
Last week, police and Army bomb disposal experts came under fire from missiles, petrol bombs, and fireworks as they carried out a security operation on the Glengalliagh Road in Derry.
As part of the three-day operation, controlled explosion was carried out on a device.
Later yesterday, a number of roads and a medical centre were closed during a security alert in the Springfield Road area of west Belfast.
Following examination part of a firearm and ammunition were identified. They had been found by a member of the public in an alleyway.
In a statement the PSNI said the items have been removed for further forensic examination.
A spokesman said: "An investigation is under way and anyone with information about this incident or who may be able to help is asked to call police at Woodbourne on the non-emergency number 101, or submit a report online using the non-emergency reporting form via http://www.psni.police.uk/makeareport/."
Police are believed to be on high alert after reports that intelligence suggests that dissident republicans had hidden a bomb in north Belfast.
The Sunday life reported sources suggesting the bomb is the New IRA hitting back at claims it is finished following the arrest of the group's alleged leadership in a sting set up by a double agent.