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5 year oldBrig-Gen Asaminew Tsige was killed as he attempted to escape from his hideout in Amhara's capital, police added.
Ethiopia's army chief Gen Seare Mekonnen was killed while trying to foil the coup, the government said.
Prime Minister Abiy Ahmed has urged Ethiopians to unite against "evil" forces set on dividing the country.
Flags are flying at half-mast after the government declared a day of mourning to mark the deaths of loyalists.
Gen Seare and Amhara governor Ambachew Mekonnen, who was also killed on Saturday, were seen as close allies of the prime minister.
A heavy contingent of pro-government forces has been deployed in Amhara's capital, Bahir Dar, and the federal capital, Addis Ababa.
The internet has been shut across the country, days after services resumed following an unexplained blackout of more than a week.
The US state department has warned its staff in Addis Ababa to stay inside.
Ethnic violence has hit Amhara and other parts of Ethiopia in recent years.
Since his election last year, Mr Abiy has transformed Ethiopia.
He has moved to end political repression by releasing political prisoners, removing bans on opposition political parties, overseeing the prosecution of officials accused of human rights abuses and has also restored diplomatic relations with Ethiopia's long-time enemy, Eritrea.
But his reforms has taken on powerful interest groups in the military and the ruling coalition.
Mr Abiy survived a grenade attack at a rally a year ago on Sunday, which killed two people and left more than 100 injured.
Africa's oldest independent country, Ethiopia is also the continent's second most populous after Nigeria, with 102.5 million inhabitants from more than 80 different ethnic groups.
A transfer hub for long-haul air travel, it has one of the fastest-growing economies in the world, but a vast number of young Ethiopians are without work.
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