"We are convinced today that it is time to realize peace in Darfur," Konare said after talks with Sudanese President Omar el- Bashir ahead of a new round of peace talks between the Sudanese government and Darfur rebel groups due to be held on Friday in the Nigerian capital Abuja.
"The next round of Abuja peace talks will be final and successful," added Konare, who paid a brief one-day visit to Sudan.
In addition, Konare reasserted that the Darfur conflict should be solved within the AU framework.
"We have confirmed that there will be no forces other than the African and the Sudanese who will handle this problem," said Konare while urging the Darfur rebels to participate in the coming talks.
For his part, Sudanese President Bashir expressed his confidence that the new round of peace talks will gain desired results against a backdrop of "positive developments in the current situations of Darfur."
Meanwhile, official Sudan News Agency (SUNA) reported that Majzoub el-Khalifa, head of the Sudanese government delegation to Abuja peace talks, said Konare and Bashir affirmed the need to pave the way for Abuja peace talks.
The two sides discussed efforts by the Sudanese government and the AU in both security and humanitarian fields in Darfur as well as the tribal reconciliations in the region, Khalifa was quoted as saying after attending the talks.
In addition, Khalifa said the coming peace negotiations will not be affected by the UN Security Council Resolution 1593 to send war crime suspects of Sudan to the International Criminal Court (ICC).
He said the Sudanese government agreed with the AU to handle complaints and violations of law concerning the Darfur conflict through the Sudanese law and the African customs.
Rebels in Sudan's western Darfur region took up arms against the government in February 2003, accusing it of neglect.
During over two years of violence, many people have been killed and more displaced.
The AU has brokered a shaky ceasefire and maintained some 2,300 troops to help keep peace and order, but the truce deal has not been translated into action on the ground.
The peace process has been stalled for the last six months as three rounds of Abuja talks made little progress.
The UN Security Council passed Resolution 1593 in March, which decides to refer war crime suspects in Darfur to the The Hague- based ICC.
Sudan rejected the resolution, saying it lacks the base of objective justice and violates its sovereignty.
The ICC launched formal investigation into suspected war crime cases in Darfur on Monday, a move the Sudanese government said was not welcome.