DNIPRO, Ukraine – Intense fighting spread Sunday into all neighborhoods in the southern port city of Mariupol, officials said, thrusting Russian and Ukrainian forces into pitched battles as Russia tries to claim its first strategic victory since invading even as its advance remains stalled in most of the country.

The urban combat included the bombing by Russian aircraft of an art school that was sheltering 400 people, according to Mariupol Mayor Vadym Boychenko. Communications in the city largely have been cut, and industrial areas linked to the city’s steel production have become a major battlefield, said Lt. Col. Sergiy Bachynskyj, a spokesman for the military hospital in Dnipro, a city about 200 miles northwest of Mariupol.

The state-sponsored media site Tass reported that Russian officials would allow armed Ukrainians to leave Mariupol unharmed during a two-hour window on Monday.

Separately on Sunday, Ukrainian President Volodymyr Zelensky renewed his position that he is willing to negotiate with Russian President Vladimir Putin. Without negotiations, it will not be possible to end the war, Zelensky said during an interview on CNN’s “Fareed Zakaria GPS.”

There are reasons to believe that the Russians and Ukrainians are still far apart on a number of major issues. Zelensky said that Ukraine would need “security guarantees, sovereignty, restoration of territorial integrity, real guarantees for our country” to end the fighting. Ukrainians are otherwise willing to defend themselves, he said.

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“They have not greeted Russian soldiers with a bunch of flowers; they have greeted them with bravery,” he said. “They have greeted them with weapons in their hands.”

The latest pronouncements come 25 days into Russia’s invasion, and as President Joe Biden and other NATO leaders prepare for a summit about the war this week in Brussels.

Zelensky has continued his near-daily campaign for more help. On Sunday during a video address to members of Israel’s parliament that aired publicly, Zelensky equated the Russian invasion of Ukraine to the Nazi campaign to subjugate Europe. He beseeched Israel to do more to prevent more carnage in his country.

“We know that you know how to protect your interests, to protect Ukrainians, and the Jews of Ukraine,” Zelensky said in a 15-minute speech broadcast from his bunker in Kyiv. “But we ask why we’re not receiving weapons from you, why you haven’t applied sanctions on Russia, and on Russian businesses. You will need to give answers, and to be able to live with those answers.”

Meanwhile, the Russian military remains bogged down in many other parts of the country, including outside Kyiv, the capital city. Western governments have assessed that thousands of Russian soldiers have been killed in Ukraine and that Russian momentum is largely stalled.

U.S. Defense Secretary Lloyd Austin said Sunday that the Ukrainian resistance, fortified by Western weapons delivered to them, has put Russian forces “into a wood chipper.” In the absence of overall success, Putin has turned to targeting “cities and towns and civilians” at long ranges in a manner that is “really disgusting,” the defense secretary said.

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But Ukrainian control of Mariupol appears to be more tenuous. When asked on CBS’s “Face the Nation” whether Russia is about to seize the city, Austin said it is “hard to say.”

“We’ve seen significant effort on their part to go after this city, go after Kyiv and other cities,” Austin said. “They really want to begin to control the population centers, but they haven’t taken it yet.”

The seizure of Mariupol would allow Putin to create a land bridge connecting the Crimean Peninsula, which Russia seized from Ukraine and annexed in 2014, with the rest Russia. It would come after Russian forces successfully occupied territory to the west of Mariupol, including in the smaller cities of Berdyansk and Melitopol.

Forceful attacks hit various cities across Ukraine on Sunday, even as Russian forces continued to face ambushes and other setbacks.

In Kyiv, munitions struck an apartment complex, blowing out windows and causing significant fire damage. Firefighters climbed through windows looking for survivors. Washington Post reporters on the scene did not witness any wounded or dead being evacuated or removed.

Britain’s Defense Ministry said Sunday that Russia was bombarding Ukraine with increasing might, causing “widespread destruction and large numbers of civilian casualties.” The “indiscriminate shelling of urban areas,” the ministry warned, could continue as Russia “looks to limit its own already considerable losses.”

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In a separate update, the ministry said the Russian naval forces continue to blockade the Ukrainian coast and launch missiles “on targets across Ukraine.” The blockade, British officials said, “is likely to exacerbate the humanitarian situation in Ukraine, preventing vital supplies reaching the Ukrainian population.”

Russian officials said Sunday that for the second time it had launched hypersonic missiles to strike in Ukraine, this time from airspace over Crimea. Such missiles fly at several times the speed of sound, making it difficult to take cover or shoot them down.

Austin played down the significance of the claims, saying that he could not confirm whether they have been used and even if they have, U.S. officials “would not see it as a game changer.”

In Turkey, Foreign Minister Mevlut Cavusoglu said that talks between Kyiv and Moscow had made some progress, with the two sides “close to an agreement on fundamental issues.”

“It is not easy to come to an agreement while civilians are dying,” he said while making a speech in the coastal city of Antalya. “Still, momentum has been gained.”

Ibrahim Kalin, an adviser to Turkish President Recep Tayyip Erdogan, said in an interview with Al Jazeera on Sunday that there was a “growing consensus” between Russia and Ukraine on some issues, including Kyiv agreeing to “neutrality” and not joining NATO. But he added that the two sides were far apart on the status of Crimea and the separatist regions of Luhansk and Donetsk in Ukraine. Given the gaps, Kalin said, Putin does not appear to be willing to meet with Zelensky.

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“The longer this takes, the more severe the damage will be for the Russian military and for the Russian economy, as well,” Kalin noted. “So I believe those will be the factors that will go into President Putin’s thinking in terms of when he will call this off.”

Turkey, a NATO member, has been forced to walk a fine line between Russia and Ukraine given its close relations with both countries. It has condemned the Russian invasion but has not joined its allies in levying sanctions. And while officials have highlighted the civilian suffering in Ukraine, they have tried to discount their country’s involvement in the war, including providing armed drones to Kyiv.

It’s unclear whether or how NATO allies may seek to expand their response to the crisis. Leaders, including Biden, have so far kept their militaries out of Ukraine while looking to demonstrate resolve. Several have repeatedly warned that if Putin expands the conflict into a NATO country, it will require a military response.

Among the countries that are the most concerned about Russia’s long-term plans are the Baltic states of Estonia, Latvia and Lithuania. Like Ukraine, they are former states. But unlike Ukraine, they joined NATO in 2004. That gives them the military alliance’s protections, which promises that other member nations will respond if there is an attack on any NATO member.

NATO Secretary General Jens Stoltenberg said Sunday that “Turkey is doing some real efforts” to facilitate talks between Ukraine and Russia, but that “it’s far too early to say whether these or other talks can lead to any concrete outcome.”

The summit this week, Stoltenberg said, will send a message that the allies are committed to preventing an escalation of the conflict into a “full-fledged war between NATO and Russia.”

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Stoltenberg reiterated on NBC’s “Meet the Press” that NATO’s “core responsibility” is to protect the 1 billion people who live in NATO’s 30 countries” – a group that does not include Ukraine.

But he acknowledged that after Russia’s invasion, NATO is faced with a “new security reality where Russia more openly contests core values of our security and are willing to use military force to achieve its objectives,” requiring the allies to build a long-term “reset of deterrence and defense.”

One idea toward that reset floated by Poland is the creation of a peacekeeping force in Ukraine. Polish Prime Minister Mateusz Morawiecki said during a news conference on Friday in Warsaw that the force could be from NATO or some other organization.

The Polish ambassador to the United States clarified Sunday that the proposal is not intended to include direct conflict with Russia, and is “understandably a preliminary concept.” The ambassador, Marek Magierowski, speaking on CNN’s “State of the Union,” did not provide a timeline for whether the peacekeepers would deploy soon or only if a settlement is reached in the war.

“I believe we have to explore every option and every avenue to stop this aggression and this unprovoked war as quickly as possible – of course without engaging Russia in direct military confrontation because that is not the intent,” Magierowski said.

The ambassador acknowledged that peacekeepers can come under attack in a war zone. “Nevertheless,” he said, “it is a proposal that should be discussed.”

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A senior Biden administration official on Sunday ruled out any U.S. military participation in a peacekeeping mission, noting Biden’s repeated promise that U.S. troops will not be in combat in Ukraine.

“The president has been very clear that we will not put American troops on the ground in Ukraine,” Linda Thomas-Greenfield, the U.S. ambassador to the United Nations, said on CNN’s “State of the Union.”

“We don’t want to escalate this into a war with the United States,” she said, adding that other NATO countries may decide to do so. “That will be a decision that they have to make.”

U.S. officials also ruled out Sunday that Biden would visit Ukraine during his visit to Europe this week. White House press secretary Jen Psaki said on Twitter that “there are no plans” to do so.

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Morris reported from Dnipro, Ukraine, along with The Washington Post’s Anastacia Galouchka, who contributed to this report. Lamothe reported from Washington, Timsit from London and Fahim from Istanbul. The Washington Post’s Siobhán O’Grady in Kyiv, Ukraine; Shira Rubin in Tel Aviv; Mary Ilyushina in Riga, Latvia; Brittany Shammas and Hannah Knowles in Washington; and Kim Bellware in Chicago contributed to this report.