Earlier on Monday, Ethiopia of attacking its heavily militarized border, but officials in Addis Ababa at the time said they had no knowledge of the reported fighting.
Ethiopian government spokesman Getachew Reda said both sides had suffered casualties but that Eritrean soldiers had "fired the first salvo" that led to the incident.
Getachew Reda did not give details on the number of casualties but warned of retaliating should Eritrea embark of what he called a "reckless move".
Speculating on why Eritrea would launch the attack, the information minister said that the country was trying to deflect attention away from a recent United Nations human rights report which accused Eritrea of committing crimes against humanity - charges it denies.
In February, Ethiopia accused Eritrea of being behind anti-government protests in the Oromia region previous year which led to a violent clampdown by the government in Addis Ababa. No death toll has been given for Sunday's clash but Getachew described the skirmish as "a major engagement".
The African Union Commissioner for Peace and Security, Smail Chergui, has appealed to Ethiopia and Eritrea to "de-escalate" a looming war situation following recent confrontations over a common border.
"They (Ethiopians) have done this and they have to stop this", Asmerom said. The continental body is ready to help Ethiopia and Eritrea "address the challenges at hand and normalize their relations", she said.
"The gathering of information from "witnesses" organised by Ethiopia allows the latter to advance its propaganda against a country that it aims to destabilise", Eritrean Foreign Minister Osman Saleh told the 47-member state forum.
In February, Ethiopia accused Eritrea of being behind anti-government protests in the Oromia region a year ago which led to a violent clampdown by the government in Addis Ababa. Please see our terms of service for more information.
Eritrea rejected the findings as "laughable".