Gen Seare and Amhara governor Ambachew Mekonnen, who was also killed on Saturday, were seen as close allies of the prime minister.
The suspected chief plotter of Saturday's failed coup attempt in Ethiopia's Amhara region has been shot dead by police.
The BBC reports, Brig-Gen Asaminew Tsige was killed on the outskirts of Amhara's capital, Bahir Dar.
Ethiopia's army chief Gen Seare Mekonnen was killed by his own bodyguard trying to foil the coup.
Gen Seare and Amhara governor Ambachew Mekonnen, who was also killed on Saturday, were seen as close allies of the prime minister.
Flags have been ordered to fly at half-mast throughout the country to honour loyalist who died in the failed coup attempt.
A heavy contingent of pro-government forces has been deployed in 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.