“There are hundreds of thousands of people, tens of thousands of children,” Zelenskyy said in a video posted to his Telegram channel. “Many refuse to leave... But it really needs to be done,” he added.
“The more people leave Donetsk region now, the fewer people the Russian army will have time to kill,” he said.
Three people died in attacks over the past day in the Donetsk region, which is partly under the control of Russian separatist forces, Gov. Pavlo Kyrylenko said on his Telegram channel.
Pledging full financial and logistical government support to evacuate the area, Zelenskyy said: “We only need a decision from the people themselves, who have not yet made it for themselves. Leave, we will help.”
His comments came as battles continued to rage around the city of Donetsk as Russia attempts to take the entire Donbas region, made up of Donetsk and neighboring Luhansk which it gained full control of earlier this month.
The Kremlin has concentrated the majority of its forces in the region since failing to take over Ukraine's capital, Kyiv, at the start of the war.
Less than 24 hours after his speech, a drone-borne explosive device detonated Sunday at the headquarters of Russia’s Black Sea Fleet, injuring six people, Russia's Black Sea Fleet’s press service said in a statement.
The explosion at the headquarters in the city of Sevastopol on the Crimean peninsula that Russia annexed from Ukraine in 2014 caused cancellation of observances of Russia’s Navy Day holiday.
Fighting also continued elsewhere in Ukraine. In the southern city of Mykolaiv, Mayor Oleksandr Senkevych said on his Telegram channel that two people were killed and three wounded by what he said was “probably the heaviest” Russian shelling “of all time.”
Oleksiy Opanasovych Vadaturskyi, the general director of Ukraine’s largest grain trading company Nibulon, and his wife Raisa Mykhailivna Vadaturska, were killed, officials later confirmed.
“Oleksiy Opanasovych did a lot for Mykolaiv region, a lot for Ukraine. His contribution to the development of the agricultural and shipbuilding industry, the development of the region, is invaluable,” the regional government said on its Telegram channel.
Elsewhere in the south, the regional governor of Dnipropetrovsk, Valentyn Reznichenko, said on his Telegram channel that at least 50 rockets hit residential areas in the city of Nikopol early Sunday.
The attacks came as both sides continued to trade blame for an attack that killed dozens of Ukrainian prisoners of war on Friday.
Russia’s defense ministry said Sunday that it had invited the United Nations and the Red Cross to investigate the site of the prison near Olenivka in Donetsk “in the interests of conducting an objective investigation.”
The ministry had published a list of 50 Ukrainian prisoners of war killed and 73 wounded in what it said was a Ukrainian military strike with a U.S.-made High Mobility Artillery Rocket System (HIMARS).
Kyiv vehemently denied any such strike and said Moscow was to blame, accusing the Kremlin of deliberately shelling the prison to falsely accuse Ukraine of war crimes and cover up its own.
NBC News has not been able to independently verify the claims of either side.
Meanwhile the U.N. had said it was prepared to send experts to investigate if it obtained consent from both parties. The International Committee of the Red Cross said it was seeking access and had offered to help evacuate the wounded.