Councillors from Clun, Bishop's Castle, Chirbury and Worthen have made the plea following what they say has been a "pronounced increase" in rural crime during the pandemic.
They have written to West Mercia police and crime commissioner John Campion.
Clun councillor Nigel Hartin said: "The Shropshire countryside has always been under-policed but now resources have been stretched to breaking point. Police officers are thin on the ground and addition now have to police the pandemic restrictions. Unfortunately criminals are taking advantage of the situation. Not only are we seeing more thefts of items from garages and out houses but even pedigree dogs are being targeted."
Bishop's Castle councillor Ruth Houghton added: "We have had issues with hare coursing for some time and our local police have been trying to combat it. Normally what we see is large numbers of people from out of the area descending on known hare habitats to carry out this illegal activity. What has only recently come to light is the linkage between this activity and other crimes such as theft from property. It seems that many come into our area not only to kill hares but also to steal."