The government says General Asamnew Tsige masterminded gun attacks on Saturday night that killed five people including the national army's chief of staff and Amhara's state president.

"The main people behind the failed coup are still at large and the security forces are hunting them," the prime minister's press secretary, Negussu Tilahun, said.

Army chief of staff Seare Mekonnen and a retired general were shot by Seare's bodyguard at his residence in the national capital Addis Ababa, the prime minister's office said.

Amhara state president Ambachew Mekonnen and an adviser were killed in the region's main city Bahir Dar, it added. Amhara's attorney general was also shot, and died of his wounds on Monday, state media reported.

Access to the internet appeared to be blocked across Ethiopia, users reported. The streets of Addis Ababa appeared calm on Monday.

Prime Minister Abiy Ahmed has pushed through sweeping changes since coming to power in April last year, making peace with Eritrea, reining in the security services, releasing political prisoners and lifting bans on some outlawed separatist groups.

The reforms in Africa's second-most populous country have won him widespread international praise.

But the premier's shake-up of the military and intelligence services has earned him powerful enemies at home, while his government is struggling to contain powerful figures in Ethiopia's myriad ethnic groups fighting the federal government and each other for greater influence and resources.

The shooting in Bahir Dar occurred when the state president - an ally of Abiy - was holding a meeting to decide how to stop Asamnew's open recruitment of ethnic Amhara militias, one Addis-based official told Reuters.

Asamnew had told the Amhara people to arm themselves and prepare for fighting against other groups, in a video spread on Facebook a week earlier.

Asamnew himself was released from prison last year after receiving an amnesty for a similar coup attempt.

Australian Associated Press