Eritrean troops spotted driving through the Ethiopian town of Adigrat, 25 km from the border, per Reuters citing witnesses and ACLED.
This is the first confirmed presence of Eritrean soldiers on Ethiopian soil since the current conflict began September 23.
ACLED says they crossed at Zelambesa and Ethiopian military drone-struck their vehicles at Guada.
Eritrea denies it, calling the reports fabricated to justify Ethiopian aggression.
Ethiopia and Eritrea severed diplomatic ties last week.
The US urged both sides to exercise restraint, warning conflict would jeopardize US cooperation with both countries.
Fears growing of a wider Horn of Africa war involving Ethiopia, Eritrea, Sudan, and Egypt.