A statement by Ethiopia's minister of Women, Children and Youth marks the first official acknowledgement of crimes activists say have been widespread.
The convoy arrived as the United Nations expressed growing alarm over the plight of Eritrean refugees in Tigray and appealed for urgent access.
The latest explosions came just hours after Ethiopian Prime Minister Abiy Ahmed declared victory in his government’s fighting against forces of the Tigray People’s Liberation Front, which runs the northern Tigray region bordering Eritrea.
There was no immediate comment from Tigray's leaders on the events in Alamata, a town near the border with Amhara regional state and around 120 km from Tigray's capital Mekelle.
At least two of the rockets hit the Asmara airport, three diplomats said, hours after the Tigray regional government warned it might attack.
Ethiopian military has "completely captured" an airport in northwest town of Humera, close to border with Sudan and Eritrea, local media report.
This year's festival witnessed significantly smaller crowds due to political tension and the Covid-19 pandemic.
Pop star Hachalu, a member of the Oromo ethnic group, Ethiopia's largest, was shot dead by unknown attackers in Addis Ababa on Monday night, fuelling ethnic tensions.
Hachalu Hundessa, famed for his political songs, came to be seen as a voice for the Oromo people during years of anti-government protest that swept Abiy to power in 2018.
Ethiopian leadership fears that Washington might brush aside their concerns and blindly favour Egypt, a country that has been identified as the main source of the Nile River for centuries.
Somali presidential spokesman Abdinur Mohamed confirms meeting, saying "It was behind closed doors and no communique is being released. It was an ice-breaking one."
The union has experienced some success in mediating conflict but it has fallen short of its stated aims.
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