Earlier, Ahmed announced the government had put down a coup attempt in the autonomous Amhara state in the country's north.
In his TV address, the prime minister said the botched coup was led by a very high-ranking regional military official and others within the country's military. Billene Seyoum, a press secretary for Ahmed, later said the coup attempt was orchestrated by General Asamnew Tsige, the region's head of security.
State media also reported that both the head of Amhara's regional government, Ambachew Mekonnen, and his adviser, were killed during the coup attempt.
"The coup attempt in Amhara regional state is against the constitution and is intended to scupper the hard-won peace of the region," the government said in a statement. "This illegal attempt should be condemned by all Ethiopians and the federal government has full capacity to overpower this armed group."
Ahmed's press secretary told journalists a "hit squad" led by Amhara's security chief burst into a government meeting on Saturday afternoon, wounding regional president Mekonnen and another top official, who both later died.
Later that evening in what appeared a "coordinated attack," the army chief and a retired general who was visiting him, were killed by his bodyguard.
Early Sunday, Brigadier General Tefera Mamo, the head of special forces in Amhara, said on TV: "Most of the people who attempted the coup have been arrested, although there are a few still at large."
"The failed coup in Amhara is the culmination of many months of ethnic and political strife," said Ludger Schadomsky, head of DW's Ethiopia language service. Internet and media access has reportedly been limited across the country. Meanwhile, internet and cybersecurity monitor group NetBlocks reported nationwide internet access was at 2 per cent of normal levels.
Ahmed, a former army intelligence officer, assumed the charge in April 2016 following three years of protests that forced former Prime Minister Hailemariam Desalegn to resign.
Ahmed has been implementing economic reforms, opened up the political sphere and prosecuted officials accused of human rights abuses. He has also established relations with neighbouring Eritrea.
However, ethnic tensions that were kept in check by the iron rule of past leaders have lead to deadly violence.