At the meeting Wednesday night in Abuja, Nigeria's capital, Obasanjo assured Konare of his confidence and those of African leaders in his capacity as chairman of the commission, the presidency said.
Disagreement between the two leaders manifested last week when Obasanjo visited Togo as part of AU efforts to help in the establishment of a government of national unity.
Obasanjo reportedly expressed surprise during the visit over the appointment of former Zambian president Kenneth Kaunda as AU mediator by Konare without consultations.
Obasanjo's spokeswoman Remi Oyo told Xinhua this week that the appointment was no longer necessary since all sides in Togo have agreed to form a unity government, noting that the disagreement did not represent crisis or split in the union.
Wednesday's meeting also discussed AU efforts toward a peaceful resolution of the crises in the western Sudanese region of Darfur, including the resumption of talks in Abuja Friday.
Meanwhile the meeting reviewed preparations toward peaceful elections in Liberia as well as flash-points in west Africa which include Cote d'Ivoire and Guinea Bissau.