The Sudanese military said the Ethiopian army displayed the bodies of the executed to the public.
The Sudanese military accused the Ethiopian army of executing seven Sudanese soldiers and one captured civilian.
In a statement on Sunday, the Sudanese military also accused the Ethiopian army of displaying the bodies of the executed in public and promised an “appropriate response”.
“This dangerous act will not pass without a response,” it said.
There was no immediate response from Ethiopian authorities to a request for comment.
Tensions between Sudan and Ethiopia have been heightened in recent years due to the spread of the virus conflict in the northern Tigray region of Ethiopia and Ethiopia built a giant hydroelectric dam on the Blue Nile.
Tens of thousands of refugees have fled to eastern Sudan, and there have been military fighting in a disputed area of farmland along the border between Sudan and Ethiopia.