The visit comes just days after a trip by UN chief Ban Ki-moon to Burundi as part of growing international efforts to bring an end to 10 months of deadly turmoil in the central African country.
The African Union agreed to send the delegation -- which is headed by South African President Jacob Zuma and includes the leaders of Ethiopia, Gabon, Mauritania and Senegal -- during its January summit when Burundi successfully faced down a plan to deploy 5,000 peacekeepers to the country.
But the main umbrella opposition group CNARED, whose leaders are in exile, dismissed it as a "false opening", saying Nkurunziza did not want real negotiations to bring peace.
The opposition was angered by the president's apparent attempt to choose who should participate when he said the dialogue would include all Burundians "except those engaged in acts of destabilisation".
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Previous talks have failed, with the Burundian government refusing to sit down with some of its opponents who it accuses of involvement in a failed coup last May and months of violence including grenade and rocket attacks.
"The issue of deploying a peacekeeping force in Burundi is not on the agenda," the diplomat added.
CNARED chairman Leonard Nyangoma welcomed the delegation's visit but held out little hope of a breakthrough.
"Nkurunziza is a diehard and without strong pressure and real sanctions he will never agree to the meaningful negotiations that are the only way out of this crisis," he told AFP by telephone.
Over 400 people have been killed since April while more than 240,000 have left the country. Violent attacks have become routine, raising fears of a return to the civil war fought between 1993-2006 in which around 300,000 people died.