Ukraine’s president Volodymyr Zelenskyy has urged residents of the country’s easternmost Donetsk region to leave the province as Russia continues its offensive to conquer the area.

In a regular nightly video address to the nation, Zelenskyy said hundreds of thousands of people were still living in the industrial heartland where “the fiercest fighting” was taking place. He told Ukrainians that an evacuation of Donetsk “needs to be done . . . now” so that “the Russian army” will kill fewer people.

Moscow is trying to take over the whole of Ukraine’s eastern Donbas region, made up of the provinces of Donetsk and Luhansk. Russian forces now occupy all of Luhansk.

The UN’s High Commissioner for Human Rights has documented more than 5,200 civilian deaths in Ukraine since Russia’s full-scale invasion began and believes more have been killed amid Russia’s bombardment of civilian areas.

Moscow has since late March refocused its war efforts on eastern Ukraine, having failed to capture the capital Kyiv in the weeks after its February 24 invasion, concentrating on taking the remaining Donbas territory, the region Russian covertly invaded in 2014.

Ukraine, using advanced weaponry supplied by the west, has been able to disrupt Russian supply lines and logistics.

Kyiv has been slowly regaining territory in the south, and the Washington-based Institute for the Study of War said in June that Ukrainian forces had liberated more territory than they had lost since the start of the invasion.

In the Russian-occupied Ukrainian peninsula of Crimea, also forcibly seized in 2014, the Russian governor of Sevastopol said on Sunday that a drone had struck the headquarters of the Black Sea fleet, wounding five people. The alleged unmanned aerial strike took place on Russia’s revered Navy Day and festivities in Sevastopol were subsequently cancelled. The Financial Times could not independently confirm the attack.

On his Telegram channel, governor Mikhail Razvozhayev said the Federal Security Service was investigating the incident.

The Black Sea fleet’s press service said “a low-yield explosive device mounted on a makeshift drone” had struck the area.

A regional Ukrainian official denied involvement in the alleged drone strike. Serhiy Bratchuk, spokesperson for the Odesa Military Administration, described the incident as a “false-flag” operation and said “Ukraine would liberate the Crimea by other means”.

In April Russia’s Moskva missile cruiser, its flagship in the Black Sea, was sunk by Ukrainian missiles.

The alleged Sevastopol strike comes after an agreement between Ukraine, Russia, Turkey and the UN was signed last week to clear maritime waterways for the export of Ukrainian grain to bordering countries.

Ukraine’s infrastructure ministry spokesperson said on Sunday that three ports in Odesa were “still waiting” for permission, as 16 vessels loaded with grain awaited departure. The shipments “probably” would start “tomorrow, but I’m not sure,” Yulia Vernyhor told the Financial Times.

Ibrahim Kalin, a senior adviser to Turkish president Recep Tayyip Erdoğan, told the broadcaster Kanal 7 that the first ship carrying Ukrainian grain was likely to depart from Odesa’s port on Monday.

“There are a couple of minor glitches and a couple of issues that are still being negotiated with the Russians. If these are sorted, the likelihood of a ship departing tomorrow morning is high . . . We will see these ships begin to leave today, tomorrow or at the very latest the next day.”

The uncertainty over the timing of the grain shipments comes as Kyiv confirmed that the owner of one of Ukraine’s biggest agricultural companies and his wife had died in overnight shelling in the southern port city of Mykolayiv.

Oleksiy Vadatursky was the founder and owner of Nibulon, a group involved in grain exports.

Neither of the warring sides has disclosed its casualty figures in the bloodiest war on the European continent since the second world war. Zelenskyy has urged the west to designate Russia a “terrorist state” in response to civilian atrocities including sexual violence, indiscriminate killing of civilians and looting.

Additional reporting by Ayla Jean Yackley in Istanbul