Police were called to an area of Hexham, Northumberland after reports were made of several sheep being killed after being attacked by dogs.
Officers attended the area known as Hermitage Tyne Green and found two dogs had chased and killed pregnant ewes.
Neighbourhood Inspector Pam Bridges said people living in the countryside near vulnerable livestock should keep fences around their property secure so dogs cannot escape.
"We want to remind dog owners to make sure their dogs are kept under control at all times, in particular when near farm land and other animals.
"Clearly failure to take simple steps to keep dogs under control in the countryside can result in sheep and other young animals being attacked, maimed or killed.
"t can also lead to dog owners losing their family pets and being prosecuted and farmers losing their animals and suffering financial loss.
"The harm in this incident caused could have been prevented if the dogs had been kept under control and out of harms way."
Police say they are appealing for witnesses and are tracing the owner of the dog with inquiries still ongoing.
Farming leaders have made repeated warnings about the dangers of dogs in areas around sheep.
Kerry Clark, NFU Scotland's Regional Manager for Lothians and Borders, said: "It is very disappointing that despite the extensive awareness raising that has taken place in recent months on this issue, a small minority of the public continue to allow their dogs to worry sheep.
"The worrying of livestock by domestic dogs can have a very damaging impact on the livelihoods of farmers, as well as cause significant and unnecessary distress to the animals themselves."
Police are appealing for witnesses and anyone with information is asked to call 101, quoting reference number 673 of 19/03/17.
