The African leaders, meeting on Monday, "agreed that they would engage" Putin and Zelensky "on the elements for a ceasefire and a lasting peace in the region," a statement from South African President Cyril Ramaphosa's office said.
"The presidents confirmed their availability to travel to Ukraine and Russia in mid June," it said.
The statement did not give a specific date or itinerary.
Foreign ministers from the respective countries will "finalize the elements of a road-map to peace," the presidency said.
The delegation unveiled by Ramaphosa last month comprises the presidents of the Republic of Congo, Egypt, Senegal, South Africa, Uganda and Zambia.
Monday's virtual meeting was also attended by Comoros President Azali Assoumani as current head of the African Union (AU).
African countries have been badly hit by rising prices of grain and the war's impact on world trade.
Observers have not lent strong gravity to the African mission, saying it is for appearances more than a viable pathway to resolving the Ukraine conflict, which began with Russia's invasion in February, 2022.