Ethiopian soldiers rest at the 5th Battalion of the Northern Command of the Ethiopian Army in Dansha, Ethiopia, on November 25, 2020. (AFP)
Sudan accused Ethiopia of capturing the soldiers on June 22 in Al-Fashaqa, a fertile strip at the centre of a hostile border disagreement between the neighbours.
Addis Ababa said Sudanese forces crossed into Ethiopian territory and the casualties resulted from a skirmish with a local militia.
"It is completely unacceptable that an allegation was made from Sudan that the (Ethiopian army) had killed (Sudanese) captives when the (Ethiopian army) wasn't present in the area," Colonel Getnet Adane, public relations director at the Ethiopian National Defense Force, told reporters on Tuesday.
"If the Ethiopian defence force had been present in the area, it would have handled (captives) in a lawful manner, which is its distinctive trait," he added, in remarks carried by the state-affiliated Fana Broadcasting Corporate.
He also said that if ordered, the army would drive Sudanese forces off any seized land "in a clear and known manner" and restore Ethiopian sovereignty.
In a statement, the army said there were casualties on both sides.
"It is known that the Defense Force is a hero that executes its responsibility lawfully and procedurally, so entities that falsely smear the army should desist from this act," it said.
Sudan recalled its ambassador to Ethiopia on Monday evening, despite Addis Ababa denying any role in the death of the soldiers.
Khartoum also vowed to lodge a complaint with the UN Security Council and regional organisations.
Relations between Khartoum and Addis Ababa have soured over Al-Fashaqa, which is close to Ethiopia's restive Tigray region.
Al-Fashaqa has long been cultivated by Ethiopian farmers but claimed by Sudan, and the dispute has sparked sporadic clashes between the Sudanese and Ethiopian sides, some fatal.
The rift over Al-Fashaqa feeds into wider tensions over land and water between the neighbours, particularly stoked by Ethiopia's mega dam on the Blue Nile.
Sudan and Egypt, both downstream countries, have been opposed to the Great Ethiopian Renaissance Dam and pushed for an agreement on the filling of its reservoir and the operation of the dam.