Some Twitter users have mocked Islamic State for the statement, claiming they are getting desperate.
One wrote: “IS would claim responsibility for anything.”
Scott Stewart wrote: “It also was not an attack targeting police as Amaq claimed, but rather a case of the perp opening fire as he was being raided.”
In the past, however, Amaq has released videos of their followers pledging allegiance to them, before carrying out attacks.
The group did so after Abdelmalik Petitjean, 19, and Adel Kermiche stormed a church in Normandy, forced 85-year-old Father Jacques Hamel to his knees and slit his throat.
Petitjean, who used the fighter name Abu Omar, was put on the terrorist watch list after trying to get to the ISIS caliphate in Syria via Turkey last month.