"Operations by federal defence forces underway in northern Ethiopia have clear, limited and achievable objectives -- to restore the rule of law and the constitutional order, and to safeguard the rights of Ethiopians to lead a peaceful life wherever they are in the country," Abiy wrote on Twitter.
His comments come after the military said Wednesday it was at war with the Tigray People's Liberation Front (TPLF) after months of tensions between Addis Ababa and the party whose leaders effectively ruled Ethiopia for three decades before Abiy took power.
Abiy appeared to be seeking to play down the bellicose rhetoric, and responded to growing international calls for dialogue between the two sides.
He said the government "patiently tried for several months to resolve differences with TPLF leadership peacefully; we tried mediation, reconciliation, dialogue.
"All failed (because) of TPLF criminal hubris and intransigence. In the last straw TPLF attacked the Northern Command based in Tigray."
Abiy, the winner of last year's Nobel Peace Prize, announced Wednesday that he had ordered military operations in Tigray in response to an "attack" by the TPLF on a military camp there.
The TPLF denies the attack occurred and accuses Abiy of concocting the story to justify deploying the military against the party.
UN chief Antonio Guterres on Friday expressed deep alarm at the situation and urged an "immediate de-escalation of tensions and a peaceful resolution to the dispute."
