"The first sign for me of the progress after the signing of the agreement is the fact that between them they have exchanged a hotline," AU representative Obasanjo told a news conference in Nairobi.
The hotline between the two sides will address any flare up in fighting and coordinate disengagements, with both sides recognizing "the challenge of fully communicating with all their units to stop fighting," an official stated.
Officials this week also want to agree membership of an African Union-led panel of experts for monitoring, verification and compliance of the ceasefire, the source familiar with the talks said.
In a press release, the African Union said the expected outcomes of the meeting "include modalities for silencing the guns, humanitarian access, and the restoration of services in the Tigray region."
Representatives of Ethiopia's government and forces from Tigray are in the Kenyan capital Nairobi to discuss how to begin implementing the ceasefire, with the talks expected to last three or four days.
Implementing the ceasefire will be tough given concerns of ongoing fighting on the ground, unsettled political and territorial disputes and an ambitious disarmament timeline.
The Tigray People's Liberation Front (TPLF), the party that dominates the region, pledged to disarm their fighters fully within 30 days under the agreement.
Former Kenyan president Uhuru Kenyatta, a co-mediator at the talks, said he hoped the parties would be able to work together to create a permanent resolution to the problem.
"We started in Pretoria, we are inching our way closer. We are now in Nairobi, we are very hopeful next time we will be in Mekelle for our (next) meeting and ultimately celebrate together in Addis Ababa," Kenyatta said, referring to the capitals of South Africa, the Tigray region and Ethiopia respectively.