The African leaders also plan to visit Russia, as a diplomatic standoff brews between South African officials and Poland.
Air raid sirens also blared in Kyiv as the visit began, the latest in a series of twists as the mission gets underway.
The leaders are expected to meet Ukrainian President Volodymyr Zelenskyy on Friday and then travel to Russia for talks with President Vladimir Putin in St Petersburg on Saturday.
The South African presidency posted footage of Ramaphosa arriving by train in the Bucha area near Kyiv after travelling from Poland.
Ramaphosa is heading a delegation, which also includes Assoumani and leaders from Zambia, Senegal, and Egypt’s prime minister.
Presidents Yoweri Museveni of Uganda, Denis Nguesso of the Republic of the Congo and Abdel Fattah el-Sisi of Egypt were also meant to go along, but they pulled out of the trip and sent representatives.
The peace mission could propose a series of “confidence-building measures” during initial efforts at mediation, according to a draft framework document seen by the Reuters news agency.
The document stated that the objective of the mission is “to promote the importance of peace and to encourage the parties to agree to a diplomacy-led process of negotiations”.
Its measures could include a Russian pullback, removal of tactical nuclear weapons from Belarus and suspension of the implementation of an International Criminal Court arrest warrant targeting Putin.
A ceasefire could follow and would need to be accompanied by negotiations between Russia and the West, the document stated.
Kyiv said its own plan, which envisages the withdrawal of Russian troops from Ukrainian land, must be the basis for any settlement of the war.
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The explosions come as a diplomatic standoff continues between South African officials and Polish authorities in Warsaw.
South Africa’s News 24 reported that the row began after a charter plane with presidential security and journalists landed in the Polish capital from Johannesburg on Wednesday night. Ramaphosa was left to travel to Kyiv by train with an unknown number of security personnel even as the plane is reportedly still stuck in Warsaw.
“A second charter plane that was apparently supposed to take the security team to a rendezvous with the president in the south of Poland before he travelled to Kyiv never arrived to pick up the South Africans upon their arrival at Warsaw’s Chopin Airport,” News 24 reported. “It is unclear who the service provider is who was to provide the second charter plane.”
According to South African journalists at the scene, Polish authorities refused to let the South African security personnel leave the plane and threatened to confiscate 13 containers of weapons and equipment on it.
In response, General Wally Rhoode, head of Ramaphosa’s security, called a press conference on the steps of the plane.
“They are delaying us,” he said, accusing Polish authorities of “sabotage” and “racism”, according to media outlet EWN. “They’re putting the life of our president in jeopardy because we could have been in Kyiv this afternoon already.”
In Kyiv, presidential spokesman Vincent Magwenya said on Twitter that the president was safe, the peace mission “is proceeding well and as planned” and South African officials were trying to resolve the stranding of the plane with Poland.