LYSYCHANSK, Ukraine —

       The mayor of Mariupol pleaded Friday for a “full evacuation” of the shattered southern Ukrainian port city that Russia now claims to control, as Moscow said it struck dozens of military targets in the sprawling eastern battle zone overnight.

       Ukraine’s military command said its troops continued to harry the forces that Russia has been massing for a full-scale assault on the Donbas, the industrial heartland where Moscow already partly holds sway. Both sides said earlier this week a new phase of combat had begun in the region, encompassing the eastern provinces of Luhansk and Donetsk.

       Russian President Vladimir Putin has said that “helping” those provinces — taken to mean seizing them — is now Moscow’s main aim.

       On Friday, a senior Russian military official said Russia also wants to control all of southern Ukraine, which would represent an expansion of Moscow’s goals. Cmdr. Rustam Minnekayev was quoted by the Interfax news agency as saying Moscow was seeking to extend its grip across Ukraine’s entire Black Sea coast, including the prized port of Odesa. It was not immediately clear, however, whether he was stating official Kremlin policy.

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       With the war in its ninth week and many eastern towns and cities in ruins, Ukrainian officials voiced fresh dismay over foundering efforts to get civilians out of harm’s way.

       The deputy prime minister, Iryna Vereshchuk, said Friday that Moscow had not agreed to any new organized evacuation of civilians from a string of ravaged eastern cities, including Mariupol, which sits in Ukraine’s southeastern corner.

       “I appeal to all those who are waiting for the evacuation: be patient,” she wrote on the Telegram messaging app. “Please hold on.”

       Three freshly dug graves are ready for the next funerals at the cemetery in Irpin, on the outskirts of Kyiv, Ukraine.

       (Emilio Morenatti / Associated Press)

       In Geneva, the United Nations’ human rights chief called on both sides to respect international human rights law, but reserved harsh criticism for Moscow amid mounting evidence of atrocities by Russian forces, including the indiscriminate bombing of populated areas and attacks on civilian infrastructure such as hospitals and schools.

       “Over these eight weeks, international humanitarian law has not merely been ignored but seemingly tossed aside,” U.N. High Commissioner for Human Rights Michelle Bachelet said.

       Her office has logged the deaths of 2,345 civilians so far, but “we know the actual numbers are going to be much higher as the horrors inflicted in areas of intense fighting, such as Mariupol, come to light,” Bachelet said.

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       On Friday, which for Eastern rite Christians is Good Friday, Ukrainian families inside and outside the main battle zone prepared as best they could to observe Easter Sunday.

       President Volodymyr Zelensky, in an overnight address to the nation, urged his compatriots to draw what strength and comfort they could from one of the most important holidays of the Christian calendar.

       “Unfortunately, Russia rejected the proposal to establish an Easter truce,” he said.

       Russian military vehicles move on a highway in an area controlled by Moscow-backed separatist forces near Mariupol, Ukraine.

       (Alexei Alexandrov / Associated Press)

       In Lysychansk, one of the few remaining cities in Luhansk province still under Ukrainian control, vendors set up a makeshift market in the foyer of a commercial strip where people could procure some of the makings for a traditional holiday meal: cheeses, kasha grains and traditional Ukrainian cured pork.

       Russia said earlier it had taken over the neighboring city of Rubizhne, but clashes continued, and Ukraine said the city had not changed hands.

       In Mariupol, where Russia is claiming military victory despite the holdout presence of hundreds of Ukrainian troops and some civilians in a giant steel plant, tens of thousands of residents remain trapped in the city in desperate conditions, municipal authorities say.

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       City officials estimate that 20,000 people have died during a siege that began in the war’s earliest days, and new satellite imagery has provided grim evidence of mass graves being filled on Mariupol’s outskirts.

       The city’s mayor, Vadym Boychenko, said on national television Friday that less than a quarter of the city’s prewar population of nearly half a million remains, and that those people — numbering about 100,000 — must be brought to safety.

       “We need only one thing: the full evacuation of the population,” said the mayor, who is not currently in the city.

       After stinging setbacks elsewhere for the Russian military — including its failure to capture the capital, Kyiv, and the loss of its Black Sea flagship to a Ukrainian missile attack — analysts said Putin probably hoped to avoid heavy troop losses that would likely have been incurred by storming Mariupol’s Azovstal steel plant, where Ukrainian troops are hunkered down together with an unknown number of civilians.

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       The vast complex is laced with tunnels and bunkers. Putin ordered Thursday that the stronghold be blockaded so tightly that “not even a fly” could enter, while portraying the battle for Mariupol as a victory for Moscow. Blockading rather than attempting to overrun the facility would free up Russian forces for deployment elsewhere in the east, a British military assessment said Friday.

       In his overnight address, Zelensky scoffed at Moscow’s victory claim, calling Mariupol “a city that continues to resist Russia, despite everything the occupiers say.”

       The Ukrainian leader also predicted that Russian forces would try to hold rigged referendums in occupied areas, aimed at pushing a false claim that Ukrainian citizens living there prefer to be under Moscow’s rule. Russia held such a referendum after seizing and annexing the Crimean peninsula eight years ago.

       Zelensky said attempted annexations in the regions of Kherson or Zaporizhzhia would lead to crippling new Western sanctions.

       “You will make your country as poor as Russia hasn’t been since the 1917 civil war,” he said, addressing Putin’s constituents directly. “So it is better to seek peace now.”

       Bulos reported from Lysychansk and King from Berlin.