The police have defended the length of time it took to respond to a 999 call in Londonderry on Wednesday night.
Three masked men, armed with guns, entered a house in the Slievemore Park area at about 2330 BST and threatened to shoot a family of three.
Ciaran Mitchell and Karen Logue said the police did not visit them until 1100 BST on Thursday.
District Commander Chief Superintendent Stephen Martin said police had to establish if the call was genuine.
"Due to concerns that this call may have been an attempt to lure police officers into the area to attack them, officers were unable to respond as fully or as quickly as they would have wished," he said.
"The safety of officers and the public is a priority for the PSNI and there are unfortunately some situations which may have to be dealt with cautiously due to the significant threat from terrorists."
Shortly after the masked men entered the home, they left for a short period of time and the couple and their five-year-old son were able to escape through a back gate.
The family said it was a case of mistaken identity.
The child's grandmother said the men pointed their guns at the five-year-old.
"He came down the stairs and he was screaming because he had heard the door being put it," she said.
"Two of the men trained their guns on the stairs, and when they saw the wee boy of five they cleared, and the other boy backed out."
The threatened man said the masked men pointed guns at his head and his chest.
SDLP councillor Shaun Gallagher has said he is unsatisfied with the police response to the incident and has made a formal complaint to the Police Ombudsman.
"You had an armed gang threatening a family's life and for whatever reason the police felt they couldn't respond," he said.
"It sends out a message that you can have a free-for-all in Shantallow and I don't think that is good enough."
Sinn Fein MLA and Policing Board member Martina Anderson said she would challenge the response time of police with the board.
"Wrong decisions such as this will only add to a lack of confidence in the PSNI and I believe there needs to be a serious re-examination of the way these judgements are made because, clearly, the PSNI got it badly wrong," she said.
Anyone with information is asked to contact police in Derry on 0845 6008000.