He and another officer died trying to prevent a coup attempt against the administration in Ethiopia's northern Amhara region, PM Abiy Ahmed said.
In Amhara itself, regional governor Ambachew Mekonnen was killed along with an adviser.
Ethnic violence has hit Amhara and other regions in recent years.
The prime minister went on TV dressed in military fatigues to denounce the attacks.
Since his election last year, Mr Abiy has moved to end political repression by releasing political prisoners, removing bans on political parties and prosecuting officials accused of human rights abuses.
The US state department has warned its staff in Addis Ababa to stay inside, saying it is aware of reports of gunfire in the city on Saturday.
Gen Seare was killed along with another general, Gezai Abera, by the bodyguard who is now in custody, the prime minister's press office said.
In Amhara the governor was killed along with senior adviser Ezez Wasie, while the region's attorney general was wounded.
Lake Ayalew has been appointed the region's acting governor.
The prime minister's office accused Amhara's regional security chief, Asaminew Tsige, of plotting the coup attempt. It was unclear whether he had been arrested.
"The coup attempt in Amhara regional state is against the constitution and is intended to scupper the hard-won peace of the region," the office added.
"This illegal attempt should be condemned by all Ethiopians and the federal government has full capacity to overpower this armed group."
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