"The dates must be confirmed," Zane Dangor, the director-general in South Africa's Foreign Affairs ministry, told lawmakers.
"But it will be early in June where the six heads of state will be shuttling between the two capitals to engage in the facilitating of peace talks or at least get towards a ceasefire."
"We have also engaged with other actors including the U.S.. There is general support for this initiative," he said.
South African President Cyril Ramaphosa announced Tuesday that Russian President Vladimir Putin and Ukrainian President Volodymyr Zelenskyy have "agreed to receive" African heads of state in Moscow and Kyiv.
Leaders of Zambia, Senegal, the Republic of Congo, Uganda, Egypt and South Africa, will lead the initiative which has been welcomed by the U.N..
South Africa, which has close ties to the Kremlin since the anti-apartheid struggle years, has refused to condemn Russia's invasion of Ukraine, saying it is "neutral" and prefers dialogue.
The peace plan bid could help Pretoria spruce up its image as a neutral player and mediator, following accusations that it has drifted towards Russia.
The announcement came a day after it emerged that South Africa's ground forces commander was in Moscow to discuss military cooperation.
It was also made days after the U.S. envoy to Pretoria accused South Africa of shipping weapons and ammunition to Russia in December. Pretoria has denied that assertion.
South Africa held controversial joint military drills with Russia and China early this year. It is also due to host a summit of BRICS (Brazil, Russia, India, China and South Africa) countries in August, to which Putin has been invited.