Flags in the capital Addis Ababa flew at half-mast after a day of mourning was announced on state television.
“All of us will remember the people who lost their lives for our togetherness and unity,” a television announcer said, reading a statement from parliament speaker Tagesse Chafo.
“It is a sad day for the whole nation. We have lost people who were patriotic. They are martyrs of peace.”
The Amhara state has declared three days of mourning after the killing in which the northern region’s leader was also killed.
The government announced a full-military funeral to be held on Wednesday in the regional capital Bahir Dar.
General Asamnew Tsige, who allegedly led the coup attempt, was shot on Monday near Bahir Dar, the prime minister’s press secretary, Negussu Tilahun, told Reuters news agency.
On Saturday afternoon, the president of Amhara, the second-largest of Ethiopia’s nine autonomous states, was in a meeting with top officials when a “hit squad” attacked, Prime Minister Abiy Ahmed’s office said.
Amhara president Ambachew Mekonnen, as well as his adviser were killed, while the state’s attorney general, who was seriously wounded, later succumbed to his injuries.
Abiy took to national television dressed in military fatigues and described the situation in Amhara as an attempted coup.
A few hours after the attack in Amhara, army chief of staff Seare Mekonnen was shot dead in his Addis Ababa home by his bodyguard, in what the government said appeared to be “a co-ordinated attack”.
An internet shutdown has been in force across Ethiopia since Saturday’s killings.
Amhara, in the northern highlands, is home to the ethnic group by the same name, and the birthplace of many of its emperors as well as the national language Amharic.
The Amhara are the second-largest ethnic grouping after the Oromo, and both spearheaded two years of anti-government protests which led to the resignation of former Prime Minister Hailemariam Desalegn.
Abiy, an Oromo, took power in April 2018 and has been lauded for a string of efforts to reform a nation which has known only the authoritarian rule of emperors and strongmen.
He has embarked on economic reforms, allowed dissident groups back into the country, sought to crack down on rights abuses and arrested dozens of top military officials.
However his efforts have unleashed deadly clashes, with ethnic tensions bubbling to the surface, and the displacement of hundreds of thousands.
Last June, Abiy escaped a grenade attack that left at least two people dead.
In October, rebellious soldiers protesting over salaries invaded Abiy’s office, but the prime minister was able to defuse the situation.