The ministry also said it had agreed to a proposal from Kyiv to open in the last 24 hours.
The Russian defence ministry announced a local ceasefire Thursday to allow civilians to be evacuated from Ukraine's besieged port city of Mariupol.
A humanitarian corridor from Mariupol to Zaporizhzhia, via the Russian-controlled port of Berdiansk, would be opened from 10 am (0700 GMT), the ministry said Wednesday.
"For this humanitarian operation to succeed, we propose to carry it out with the direct participation of the UN High Commissioner for Refugees and the International Committee of the Red Cross," the ministry statement said.
The Russian ministry asked Kyiv to guarantee the "unconditional respect" for the ceasefire through written notification to the Russian side, the UNHCR and ICRC before 6 am (0300 GMT) Thursday.
Moscow also asked the Ukrainian army to commit to ensure the security of the bus convoys along the designated corridor.
The ministry also said it had agreed to a proposal from Kyiv to open in the last 24 hours four new humanitarian corridors from Mariupol to Zaporizhzhia.
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