AU chair Moussa Faki said he was following reports of escalating violence in Tigray with grave concern.
"The chairperson strongly calls for an immediate, unconditional ceasefire and the resumption of humanitarian services," the AU said in a statement.
AU-led peace talks proposed for earlier this month were delayed for logistical reasons.
Tigray authorities said their forces would abide by an immediate truce.
"Efforts to bring about a cessation of hostilities underscore the gravity of the humanitarian catastrophe," they said in a statement.
Ethiopia's government on Monday recommitted to peace talks but did not address African Union appeals for a ceasefire as fighting rages, vowing "defensive measures" including seizing airports and other federal facilities in Tigray.
"These measures are necessitated not only by the repeated attacks of the TPLF (Tigray People's Liberation Front) but also by its active collusion with these hostile foreign powers," the Government Communication Service said in a statement, without naming those powers.
The Ethiopian government said Monday it "deeply regrets" any harm to civilians and humanitarian staff, after a deadly attack in Tigray last week that claimed the lives of three civilians including an aid worker.
"The Government of Ethiopia deeply regrets any harm that might have been inflicted on civilians, including humanitarian personnel," the Government Communication Service said, adding that it would investigate such incidents.
Ethiopia aims to seize airports and other key infrastructure in the north of the country currently under the control of Tigray regional forces, the government said on Monday even as it stated it wanted a negotiated solution.
"It is ... imperative that the government of Ethiopia assumes immediate control of all airports, other federal facilities, and installations in the region," the government communication service said in a statement.
While pursuing these objectives, it said, the government was committed to a peaceful resolution of the conflict through African Union-led peace talks.
U.S. development agency USAID chief Samantha Power on Sunday joined the call for the joint offensive by Ethiopian federal forces and Eritrean Defence Forces (EDF) to stop.
"With as many as one million people teetering on the edge of famine, we urge all parties... to agree to a ceasefire, and call for safe and unhindered humanitarian access and withdrawal of the EDF from Ethiopia," Power wrote on Twitter.
Eritrean Information Minister Yemane Gebremeskel did not respond to requests for comment.
This report contains information from Reuters and Agence France-Presse