In a social media post late Thursday, Vereshchuk urged the people in Mariupol to "assemble in front of the Port-Citi shopping mall at 12 noon", Ukrayinska Pravda reported.
The Minister's announcement came just hours after UN Secretary-General Antonio Guterres said that the third phase of evacuation of civilians from the Azovstal plant, the last stronghold of the Ukrainian troops in Mariupol, had started.
Addressing the Security Council, the UN chief said: "The third phase of an operation to rescue Mariupol civilians is currently underway. But our policy is not to disclose its details until the operation is over so as not to disrupt it.
"So far, nearly 500 civilians have been rescued (during the previous two phases of evacuation) and transported to safe places after having survived under relentless artillery shelling and having endured a lack of food, drinking water, and medicine."
Guterres said that representatives of the UN and the International Committee of the Red Cross were conducting a complicated operation and coordinating their actions with both the Ukrainian government and Russian forces.
The Secretary-General expressed hope that in the future a ceasefire will be reached so as to enable civilians in other hotspots to be rescued.
Earlier on Thursday, Martin Griffiths, the Under-Secretary-General for Humanitarian Affairs and Emergency Relief Coordinator at the UN, had announced that a new convoy of buses had set out for the Azovstal plant, reports Ukrayinska Pravda.
He said the buses will take the remaining 200 civilians from the war zone.
On Sunday, the Ukrainian government, aided by the UN and the ICRC, was able to evacuate some of the civilians who were hiding in Azovstal bunkers.
The evacuation convoy arrived to Zaporizhzhya on Tuesday.
The following day, 344 civilians were evacuated to Zaporizhzhya via the "Mariupol corridor", as part of the second phase of the evacuation operation facilitated by the UN and the ICRC.
However, the remaining Ukrainian forces inside the steel plant, including fighters from the Azov regiment, said on Thursday night that Russian troops were still continuing with artillery shelling and air strikes.