Officers searching for the missing Staffordshire bull terrier cross in north Shropshire are working with a civilian group, Canine Capture, in further attempts to find the animal.
They say they do not wish the dog any harm but have a duty to protect the public after incidents in which the dog bit an experienced handler and, while unattended, tried to attack a group of children in Shrewsbury last month.
Officers say that because the dog is very scared it could react aggressively but they stressed they did not consider it to be dangerous simply because of its breed.
The dog was reported missing from private kennels near Whitchurch on Monday, where it had been boarding since July 16 following an incident in which a police officer was bitten.
The officer, an experienced dog handler, suffered puncture wounds and bruising to his thigh and needed hospital treatment following an incident in Shrewsbury but he is now fully recovered.
In a statement West Mercia Police said: "Police had been called to the Shrewsbury street by a member of the public who reported that an unattended dog had tried to attack a group of children.
"Officers were able to catch the dog and it was taken to kennels."
They said the dog escaped from the kennels this week and despite sightings by members of the public in the village of Hollinwood, near Whitchurch, it has evaded capture.
Chief Inspector Tracy Ryan from the Shropshire Command Team said: "This dog has been on the run for a few days now and it is likely that he is very scared and therefore his reactions will be unpredictable. The longer this goes on the more frightened he will become and the higher the risk.
"We do not want to frighten members of the public but we do want to be very clear that if they try to approach the dog it could react aggressively and we do not want them to put themselves at risk.
"If you see the dog call 999 immediately so that we and our civilian experts can take appropriate action.
"We do not wish the dog harm but we have a duty to protect the public."