Mariupol mayor Vadym Boichenko has said that an evacuation convoy has begun moving from the coastal town of Berdiansk, some 50 miles (85 kilometers) west of the besieged city, towards territory held by Ukraine.
The convoy includes many of the first batch of people to have been evacuated from the Azovstal steel plant.
"Now the column is moving in the direction of Zaporizhzhia. This evacuation is still ongoing, so we provide very limited information," Boichenko said on Ukrainian television.
"We expect that it will work, that our residents, those who hid for more than two months on Azovstal, will get to the territory controlled by Ukraine."
Boichenko was less optimistic about the people still trapped in Azovstal.
"Civilians remain at Azovstal. Unfortunately, destruction are being added there. Both enemy artillery and aircraft hit these facilities yesterday," Boichenko added.
"They are also waiting to be evacuated. More than 200 locals are still hiding in the area. And also there our [military] guys continue to defend Mariupol, our state."
Boichenko said it remained very difficult for thousands of people in Mariupol to leave Russian controlled territory. He said 2,000 residents remain stranded in the Berdiansk area.