The image at Junior McDaid House in the city’s Chamberlain Street is accompanied by a verse implying that members of the security forces had “better watch out” and “stop harassing our kids” because “Santa Claus is coming to town”.
It appears to be a reference to comments made by Chief Constable Simon Byrne earlier this year, when he suggested the children of paramilitaries could be taken into care.
Chief Inspector Jonny Hunter said the display is now under investigation.
He said: “We are aware of the crude and utterly distasteful display along with the false commentary attached to the post on social media.
“The image of Santa carrying a gun is truly despicable especially given the proximity of the premises to the city centre and the fact that many young children are likely to view it. While we haven’t received any reports at this stage from members of the public we are making enquiries to establish if any offences have been committed.”
The Police Federation which represents rank and file officer said the PSNI in Derry will be undeterred by the threat contained in what it called the “reprehensible message”.
A spokesman said: “I have no doubt that the good people of Derry will treat this display with the contempt it deserves.
“It is a sick gesture, made all the worse because they use the festive period – a period of peace and goodwill – to spread their sad and reprehensible message.
“People throughout Derry, indeed throughout Northern Ireland, want to be rid of these people and build better lives for themselves and their children.
“They are attempting to control and hold back a community that has suffered enough.“Officers will continue to police all parts of the city, exercising caution but undeterred in their commitment to deliver a professional and respectful service to people who want the legitimate rule of law and not the law of thugs and bullies.”
Junior McDaid House is the headquarters of Saoradh, the political wing of the New IRA who shot dead journalist Lyra McKee on Thursday, April 18 in Creggam.
The Santa Claus window painting is not the first time such an image has appeared on the window of Junior McDaid House.
In 2017 a Snowman was depicted armed with an RPG 7 rocket launcher with the message “Wishing you an explosive Christmas”.
A police investigation was followed by charges being brought against two men, however judge Barney McElholm dismissed the case due to a lack of legislation.
The window display was also condemned by Ann Travers, a friend of Lyra McKee.
Ms Travers’ sister Mary was murdered by the IRA and her father Tom seriously injured in the same gun attack as they left Mass in south Belfast.
She said: “This is just horrible, this is the associates of the people who murdered my friend Lyra. Her mum lost her child because of them and this will be her first Christmas without her youngest child.
“This will be so incredibly painful to Lyra’s family and to Lyra’s partner Sara Canning.
“Lyra loved Christmas, she was always buying presents, she was generous to a fault so for these people who were responsible for her death to taint something she loved shows them for the monsters they are.
“Christmas is all about children and family and it is about tolerance and respect but for someone to paint the window of their premises with such a depraved message there must be something seriously wrong with them.
“The irony is I think they are the people who are harassing and abusing children by selling them these romanticised tall tales of saving Ireland when, in reality, they are snaring them into a hopeless cause that no one supports or wants.”