Ethiopian forces have taken measures against the forces that are believed to be trained and supported by Eritrea, Assefa Abiyu of the Ethiopian Federal Police Commission told the state-affiliated Fana Broadcasting Corporation. He added that a number of them have been arrested.
He did not say when the killings took place and the nationalities of the victims remained unclear.
"The forces tried to enter into Ethiopia from the western part of the Tigray Region. We have managed to control their movement and attack them without letting a single one of them escape," Abiyu said.
The killings follow warnings by Ethiopian Prime Minister Hailemariam Desalegn, who told lawmakers on Tuesday that Ethiopia will take measures to punish the Eritrean government if it feels provoked.
Ethiopia has no diplomatic ties with Eritrea, which broke away from Ethiopia in 1991 after a civil war that lasted three decades.
Ethiopia has struck inside the Eritrean territory in the past, saying some armed groups are using Eritrea as a staging ground for attacks against Ethiopia.
Eritrea in turn accuses Ethiopia of harboring groups opposed to the Eritrean government.