If held, the talks would be the first formal negotiations between the two sides since the outbreak of war in November 2020.
Both sides had previously said they were prepared to participate in AU-mediated talks, but intense fighting has continued to rage across Tigray.
Tigray's forces have yet to respond to the invitation for talks this weekend in South Africa.
Prime Minister Abiy Ahmed's national security advisor said on Twitter on Wednesday (October 5) they had accepted the invitation, adding the talks needed to be without preconditions.
In a letter seen by Reuters, AU Commission Chair Moussa Faki also invited Debretsion Gebremichael, who leads Tigray's ruling political party, to the talks.
The letter was dated Oct. 1, but a spokesman for Debretsion's Tigray People's Liberation Front - or TPLF - said on Tuesday (October 4) that he was not aware of any imminent talks.
The spokesman also did not immediately respond to a request for comment on Wednesday about the Ethiopian government's acceptance of the invitation.
Last month the TPLF said it was ready for a ceasefire, adding that it would accept an AU-led peace process.
Previously it had objections to AU proposals.
The government accuses the TPLF, which dominated the country's ruling coalition until Abiy came to power in 2018, of trying to reassert Tigrayan dominance over Ethiopia.
The TPLF accuses Abiy of over-centralizing power and oppressing Tigrayans.
Both dismiss each other's accusations.
The conflict has killed thousands of civilians and uprooted millions.
