The war in northern Ethiopia erupted in November 2020. AFP
Prime Minister Abiy Ahmed's national security adviser Redwan Hussein said on Twitter that the government had "accepted this invitation which is in line with our principled position regarding the peaceful resolution of the conflict and the need to have talks without preconditions".
Both sides have been invited to talks in South Africa this weekend, according to a letter written by AU chair Moussa Faki Mahamat, and forwarded to AFP by the foreign ministry in Pretoria.
The Government Communication Service said in a statement that the AU had set "both the date and the venue" for the talks but did not elaborate.
AU spokeswoman Ebba Kalondo declined to provide information about when and where the talks would take place, telling AFP: "We will communicate details as and when appropriate", adding that the process remained "on track".
The deepening conflict has raised international alarm, with the United States this week announcing that its special envoy to the region, Mike Hammer, would be making his second visit to Ethiopia in as many months to seek a halt to the fighting.
The latest upsurge has also drawn Eritrean troops back on to the battlefield in support of Ethiopia's federal and regional forces, which are fighting the TPLF on multiple fronts in the country's north.
'Troika Of Negotiators'
A diplomatic source told AFP that the AU talks would be mediated by "a troika of negotiators" including the bloc's Horn of Africa envoy Olusegun Obasanjo and former Kenyan president Uhuru Kenyatta.
Another diplomatic source said South Africa's former deputy president Phumzile Mlambo-Ngcuka would serve as the third negotiator.
The warring sides were previously at odds over who should mediate negotiations, with Abiy's government pushing for Obasanjo and the TPLF wanting Kenyatta to broker dialogue.
They have also sparred over the restoration of basic services such as electricity, communications and banking in Tigray -- a key precondition for dialogue according to the TPLF.
The region of six million people has been facing desperate shortages of food, fuel, medicines and other emergency supplies, with the UN's World Food Programme warning of rising malnutrition even before the latest fighting halted aid deliveries.
The US State Department on Monday announced that special envoy Hammer would travel to Kenya, South Africa and Ethiopia this month.
The visit, which will include meetings with federal government and African Union officials, comes on the heels of an 11-day trip by Hammer to Ethiopia last month, with the State Department saying it was aimed at supporting the launch of AU-led peace talks.
The war, which erupted in November 2020, has killed untold numbers of civilians and triggered a deep humanitarian crisis, and all sides to the conflict have been accused of grave abuses against civilians.
The TPLF dominated Ethiopia's ruling coalition for decades before Abiy took power in 2018.
After months of rising tensions, Abiy sent soldiers into Tigray to unseat the TPLF, saying the move was in response to attacks on federal army camps.