Speaking to The Irish News, Assistant Chief Constable Mark McEwan said the PSNI sought to “reassure that we are looking at the threat and seeking to corroborate it”.
“We are taking it seriously and just remind people to take reasonable steps around their security on and off duty,” he added.
“They are well used to these sorts of messages anyway.
“Any specific concerns, we will deal with those.”
The message was sent on Monday after republican group Arm na Poblachta said in a statement: “We are now looking at the families of PSNI officers as legitimate targets.
“The PSNI have targeted republican sympathisers, now republicans will target family members of PSNI officers.”
It is understood that the children of serving officers are not included in the threat.
The group also claimed responsibility for a suspect device found in the Corrody Road area of Derry on February 18.
The device was found metres away from playing children and houses, but was declared an “elaborate hoax” by the PSNI.
Arm na Poblachta claimed that the device was partially disassembled after the operation was “abandoned.”
This fresh warning to PSNI officers comes after the shooting of DCI John Caldwell in Omagh on February 22.
He was shot by gunmen while coaching a children’s football game. His son was part of the coaching group.
The New IRA claimed responsibility for the attack but was assisted by loyalist criminals in targeting DCI Caldwell and supplying two guns used in the attack.
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