Two homes in the Markethill area were targeted by thieves overnight.
Police have issued a warning for residents to be vigilant following the incidents in the Mowhan Road area of the town.
A police spokesperson said: “A report was received shortly after 3am that an attempt had been made to gain entry to a house in the Pinley Green area.
“Damage was caused to the lock on the back door of the house but no entry was gained. A further report was received on Friday morning that a house in the Mount Pleasant area of the town had been broken into sometime overnight.
“Cupboards and drawers in the house had been rifled through but it is unclear at this time if anything was taken.”
Alderman Gareth Wilson has also spoken of his concerns.
The Cusher ABC Council DUP representative stated: “This is obviously concerning for residents and I understand that two homes were targeted in these incidents, one in Pinley Green and one in Mount Pleasant close by.
“From discussions with police the thieves attempted to gain entry to one property and did gain entry to the other causing some disruption to items within the home.
“I would reiterate the advice of the PSNI locally for residents to remain vigilant and to also ensure windows and doors are secured at night and that valuables are hidden out of sight and easy reach of criminals.”
He added: “Criminals spend their days planning their next act of criminality and it is always the law abiding and peaceful public who are the targets.”
Anyone with any information or who may be able to help with the investigation, is asked to call officers in Armagh on the non-emergency number 101, quoting reference number 258 11/10/24, or submit a report online using the non-emergency reporting form via http://www.psni.police.uk/makeareport/.
You can also contact Crimestoppers anonymously on 0800 555 111 or online at http://crimestoppers-uk.org/.
“If anyone witnessed anything suspicious in the area around 3am this morning they should report this immediately to the PSNI using the 101 telephone number.”
