Lviv, Ukraine — Ukrainian President Volodymyr Zelenskyy on Saturday called for direct talks with Russian President Vladimir Putin as Russian forces pushed deeper into the beleaguered southern port city of Mariupol, with heavy street battles shutting down a major steel plant and hampering rescue efforts.

Military skirmishes erupted across the heart of Mariupol’s city center, obstructing local efforts to rescue hundreds of people believed to be trapped in the basement of a theater struck by a bomb or missile Wednesday. Russia denied bombing the theater, where hundreds of people — mostly women, children and the elderly — were reported to have sought refuge.

“The city is leveled to the ground,” a member of the Azov regiment that is defending Mariupol said Saturday on Telegram as tanks moved in and Russian forces continued to strike from the air.

Meanwhile on Saturday, the Russian military said it had deployed its Kinzhal, or Dagger, aviation missile system with hypersonic aero-ballistic missiles — high-speed weapons that can fly at 10 times the speed of sound and elude missile defense systems — for what is believed to be the first time since troops were deployed.

A spokesman for the Russian Defense Ministry, Maj. Gen. Igor Konashenkov, said in a video posted on state media RIA’s Telegram channel that the missile system was used Friday to destroy a large underground warehouse containing weapons and ammunition in the village of Delyatyn, about 380 miles west of the capital, Kyiv.

Putin has boasted of his military’s investment in hypersonic missiles. In December, he said that Russia was the global leader in such weapons and that it would probably remain ahead by further advancing its technology before the U.S. caught up.

In a video address early Saturday, Zelenskyy repeated his desire to personally hold talks with Putin as the war in Ukraine raged on for a fourth week amid a stream of refugees, a widening humanitarian crisis and fruitless cease-fire talks. “It’s time to meet, time to talk,” Zelenskyy said.

Russian military commanders’ “cruel and erroneous tactics” of targeting civilians and destroying apartments, hospitals and churches, Zelenskyy said, had failed and led only to harsh sanctions. In the absence of a peace settlement, he said Russia could face “such losses that several generations will not be enough for it to rise back up.”

Fighting and shelling continued Saturday on several fronts throughout the country, even as Ukrainian authorities said that Moscow and Kyiv had agreed to the creation of 10 humanitarian corridors to evacuate residents from cities under attack, including Kyiv and Mariupol, the strategic port city of nearly 450,000 on the coast of the Sea of Azov.

“Children, elderly people are dying,” Mariupol police officer Michail Vershnin said in a video as he stood amid a street filled with rubble, according to the Associated Press. “The city is destroyed and it is wiped off the face of the Earth.”

Some of the fiercest fighting reported Saturday in Mariupol was for control of the Azovstal steel plant, one of the largest in Europe, said Vadym Denysenko, an adviser to Ukraine’s interior minister. Russia’s true aim is not only the “demilitarization” of Ukraine, but also the deindustrialization of the country, Denysenko said.

Mariupol’s City Council said that Russians had begun to round up residents from the city’s Left Bank district and shelters in the last few days and deport them to Russia by force. Captured Mariupol residents were taken to camps where the Russians inspected their phones and documents, the council said in a statement on Telegram. Some were redirected to remote cities in Russia; the fate of others was unknown.

“What the invaders are doing today is familiar to the older generation, who saw the horrific events of World War II, when the Nazis forcibly captured people,” Mayor Vadym Boychenko said. “It is hard to imagine that in the 21st century people would be forcibly deported to another country.”

In Mykolaiv, a major Black Sea port and shipbuilding center about 300 miles west of Mariupol, rescuers used shovels and their bare hands to search for survivors from the rubble of a barracks housing soldiers after a missile struck several buildings on Friday. Dozens of troops are reported to have been killed in the attack by Russian forces, according to a report from the Swedish publication Expressen.

Zelenskyy has accused Russia of blockading large cities in central and southeastern Ukraine — preventing the delivery of food and other supplies — in a bid to force inhabitants to capitulate. Putin has denied targeting civilians during the invasion.

Russia continued to make “incremental gains” in Ukraine’s south, targeting civilian populations with “brutal, savage techniques,” U.S. Secretary of Defense Lloyd J. Austin III said Saturday, during a joint news conference in Sofia with Bulgaria’s Prime Minister Kiril Petkov.

“The amount of pain that the civilians have endured ... has been hard to watch,” Austin said.

Faced with fierce resistance from Ukraine, Russia had been forced to change its operational approach and “is now pursuing a strategy of attrition,” the U.K. Ministry of Defense said Saturday in an intelligence update.

“This is likely to involve the indiscriminate use of firepower,” it added, “resulting in increased civilian casualties, destruction of Ukrainian infrastructure, and intensify the humanitarian crisis.”

James Acton, a co-director of the Nuclear Policy Program at the Carnegie Endowment for International Peace, said that the use of the Kinzhal aviation missile system comes after the Russians had already used the Iskander, a ground-launched version of the hypersonic ballistic missile, during the conflict.

Rather than a show of Russian strength, Acton said, the deployment of the Kinzhal could be a sign of how badly the conflict was going. “I suspect it’s a reflection of the fact that they’re running low on accurate munitions,” he said.

“At a time when they’re killing children and civilians in schools and hospitals, a strike against a legitimate military target with this weapon is a drop in the bucket.”

Video images have shown long lines of vehicles fleeing Mariupol For Russia, experts say, Mariupol is a vital target: Its capture could help facilitate coordination and joint operations between Russian-backed rebels in eastern Ukraine and Russian forces in Crimea, which was annexed by Moscow in 2014.

Images from the city have revealed a broad panorama of destruction — entire apartment blocks and a shopping center, as well as the theater housing those seeking refuge, ravaged by attacks. A strike Monday on a maternity hospital killed at least five people and left more than a dozen injured, authorities said. Residents remaining in Mariupol are struggling to find food and water, and much of the city lacks electricity and residential heating, despite freezing temperatures, Ukrainian officials say.

“There are tanks... and artillery shelling, and all kinds of weapons fired in the area,” Boychenko told the BBC. “Our forces are doing everything they can to hold their position in the city,” he added, “but the forces of the enemy are larger than ours, unfortunately.”

On Saturday night, Ukraine’s Foreign Minister Dmytro Kuleba posted a satellite photo of the ruins of Mariupol’s Donetsk Regional Theatre of Drama. About two-thirds of the large modern building was destroyed with only the western facade left standing.

On the ground, outside the entrance, the word "Дети" — Russian for “children” — had been painted in large white letters in an attempt to dissuade Russia from striking.

“Inhuman Russian war crime,” Kuleba said. “I want to ask multinational companies still working with or in Russia: how can you keep doing business with them? How can you feed, serve, and pay those who did this?”

In a video address early Saturday, Zelenskyy said that some 130 people had escaped or been rescued from the theater, some seriously wounded, and people were still being rescued from the rubble.

More than 9,000 people had been able to leave Mariupol in the previous 24 hours, Zelenskyy said. Throughout Ukraine, he said, more than 180,000 have been able to escape via humanitarian corridors.

A convoy of buses carrying about 500 people who had left Mariupol on Friday arrived in Zaporizhzhia on Saturday, Kirill Tymoshenko, deputy head of the presidential office, said on Telegram. Those who wanted to immediately continue evacuating would be sent on to the railway station, he said, while those who preferred to rest would be placed in a kindergarten and evacuated later.

Deputy Prime Minister Iryna Vereshchuk urged residents of the village of Bervytsya, about 40 miles northeast of Kyiv, to walk four miles to the bridge in the nearby village of Mokrets and cross the Trubizh River to meet buses that would take them to Brovary.

“Residents of settlements, please be attentive,” Vereshchuk said. “Because it is extremely difficult to open the corridors, the enemy insidiously breaks our agreements. Please, if there is an opportunity, use it today.”

At least 847 civilians, including 64 children, have been killed in Ukraine since the war began, the United Nations Human Rights Office said in a Saturday report. An additional 1,399 civilians have been injured, including 78 children.

“Most of the civilian casualties recorded were caused by the use of explosive weapons with a wide impact area, including shelling from heavy artillery and multiple-launch rocket systems, and missile and air strikes,” the Office of the U.N. High Commissioner for Human Rights said. The actual figures are likely to be considerably higher, it noted, especially in Russian-controlled territory and cities, such as Mariupol and Volnavakha, where intense hostilities led to information delays.

Almost 6.5 million people have been displaced throughout Ukraine, the United Nations said Friday, and some 3.2 million have fled the country. Those estimates indicate that close to one-quarter of Ukraine’s 44 million residents have fled their homes, even as thousands continue to escape the violence, heading both abroad and to areas perceived as safe within Ukraine.

Zelenskyy’s plea to meet with Putin is his latest bid to have direct talks with the Russian leader, who on Friday made a celebratory appearance at a stadium in Moscow, marking Russia’s annexation of the Crimea peninsula from Ukraine.

During the rally, Putin repeated his assertion that the war, which he refers to as a “special operation,” has been necessary to stop the “genocide” of Russian speakers in Ukraine, a claim soundly rejected by Ukrainian officials.

Negotiations between Ukraine and Russia have taken place every day this week, with no agreement on an end to the fighting. Earlier in the week, representatives for both sides cited progress in the talks, but in a call Friday with German Chancellor Olaf Scholz, Putin accused the Ukrainians of stalling. A readout of the conversation in TASS, the Russian state-owned news agency, said the Russian leader accused the “Kyiv regime” of trying to delay negotiations by “putting forward more and more unrealistic proposals.”

Putin has insisted that his demands — including Ukraine’s “demilitarization” and its renunciation of any intention to join NATO or the European Union — be completely fulfilled before any cessation of armed hostilities.

Pursuit of NATO membership is enshrined in Ukraine’s constitution, but Zelenskyy shifted on the issue this week, saying he accepts that the country will not join the U.S.-led alliance.

Zelenskyy tweeted Friday that Ukraine retains aspirations to join the European Union, saying he had a “substantial conversation” with Ursula von der Leyen, the president of the European Commission, the EU’s executive arm. Zelenskyy said the commission’s “opinion on [Ukrainian] application for EU membership will be prepared within a few months.”

In Lviv on Saturday, air raid sirens sounded a day after what authorities called a Russian strike on an aircraft maintenance facility next to the airport. No one was killed in Friday’s attack, officials said, but it was the first strike within the city limits of Lviv — a western city that is a key hub for both displaced persons from the war and for supplies entering Ukraine from Poland, a NATO member just 40 miles to the west.

Still, despite the attack, life went on at its normal pace Saturday in Lviv, which has been insulated from the extreme violence seen in Kyiv, Mariupol and other cities.

As sirens wailed in the late afternoon, residents went about their business, strolling and taking coffee rather than taking shelter as directed.

On Friday, residents placed 100 baby carriages in a central square of this ancient city to symbolize the reported deaths of more than 100 children since the Russian invasion began.

Los Angeles Times staff writer Tracy Wilkinson in Washington contributed to this report.