Ukrainian officials defiantly rejected a Russian demand that their forces in Mariupol lay down arms and raise white flags Monday in exchange for safe passage out of the besieged strategic port city.

Russia has been barraging the encircled southern city on the Azov Sea, hitting an art school sheltering some 400 people only hours before offering to open two corridors out of the city in return for the capitulation of its defenders, according to Ukrainian officials.

Fighting for Mariupol has remained intense, even as the Russian offensive in other areas has floundered to the point where Western governments and analysts see the broader conflict grinding into a war of attrition.

Ukrainian officials rejected the Russian proposal for safe passage out of Mariupol even before Moscow's 5 a.m. deadline for a response came and went.

"There can be no talk of any surrender, laying down of arms," Ukrainian Deputy Prime Minister Iryna Vereshchuk told the news outlet Ukrainian Pravda. "We have already informed the Russian side about this."

Mariupol Mayor Piotr Andryushchenko also rejected the offer shortly after it was made, saying in a Facebook post he didn’t need to wait until the morning deadline to respond and cursing at the Russians, according to the news agency Interfax Ukraine.

Russian Col. Gen. Mikhail Mizintsev had offered two corridors – one heading east toward Russia and the other west to other parts of Ukraine. He did not say what Russia planned if the offer was rejected.

The Russian Ministry of Defense said authorities in Mariupol could face a military tribunal if they sided with what it described as "bandits," the Russian state news agency RIA Novosti reported.

Earlier attempts to evacuate civilian residents from Mariupol and other Ukrainian cities have failed or only partly succeeded, with bombardments continuing as civilians sought to flee.

Tearful evacuees from devastated Mariupol have described how "battles took place over every street."

Ahead of the latest offer, a Russian airstrike hit the school where some 400 civilians had been taking shelter and it was not clear how many casualties there were, Ukraine’s President Volodymyr Zelenskyy said in a video address early Monday.

"They are under the rubble, and we don’t know how many of them have survived," he said.

The fall of Mariupol would allow Russian forces in southern and eastern Ukraine to unite. But Western military analysts say that even if the surrounded city is taken, the troops battling a block at a time for control there may be too depleted to help secure Russian breakthroughs on other fronts.

Ukrainians "have not greeted Russian soldiers with a bunch of flowers," Zelenskyy told CNN, but with "weapons in their hands."

Three weeks into the invasion, the two sides now seem to be trying to wear down the other, experts say, with bogged-down Russian forces launching long-range missiles at cities and military bases as Ukrainian forces carry out hit-and-run attacks and seek to sever Russian supply lines.

"The block-by-block fighting in Mariupol itself is costing the Russian military time, initiative, and combat power," the Washington-based Institute for the Study of War said in a briefing.

U.S. Defense Secretary Lloyd Austin said Ukrainian resistance means Russian President Vladimir Putin’s "forces on the ground are essentially stalled."

"It’s had the effect of him moving his forces into a woodchipper," Austin told CBS on Sunday.

The strike on the art school was the second time in less than a week that officials reported an attack on a public building where Mariupol residents had taken shelter. On Wednesday, a bomb hit a theater where more than 1,000 people were believed to be sheltering.

There was no immediate word on casualties in the school attack, which The Associated Press (AP) could not independently verify. Ukrainian officials have not given an update on the search of the theater since Friday, when they said at least 130 people had been rescued and another 1,300 were trapped by rubble.

City officials and aid groups say food, water and electricity have run low in Mariupol and fighting has kept out humanitarian convoys. Communications are severed.

The city has been under bombardment for over three weeks and has seen some of the worst horrors of the war. City officials said at least 2,300 people have died, with some buried in mass graves.

Some who were able to flee Mariupol tearfully hugged relatives as they arrived by train Sunday in Lviv, about 1,100 kilometers (680 miles) to the west.

"Battles took place over every street. Every house became a target," said Olga Nikitina, who was embraced by her brother as she got off the train. "Gunfire blew out the windows. The apartment was below freezing."

In Ukraine’s major cities, hundreds of men, women and children have been killed in Russian attacks.

In Kyiv, eight people were killed by shelling in the densely populated Podil district not far from the center of the capital Sunday, according to AP journalists at the scene. It devastated a shopping center, leaving a flattened ruin still smoldering Monday morning in the midst of high-rise towers. The force of the explosion shattered every window in the high-rise next door and twisted their metal frames.

In the distance, the sound of artillery rang out as firefighters picked their way through the destruction. Kyiv Mayor Vitali Klitschko said Russian shelling hit several houses in Podil.

Russian troops have been shelling Kyiv for a fourth week now and are trying to surround the capital, which had nearly 3 million people before the war.

In the southern city of Kherson, video seen by Reuters showed dozens of protesters, some wrapped in Ukraine's blue-and-yellow flag, chanting "Go home" in Russian at two military vehicles with Russian markings. The vehicles turned and left.

"I want the war to be over, I want them (Russian forces) to leave Ukraine in peace," said Margarita Morozova, 87, who survived Nazi Germany's siege of Leningrad in World War II and has lived in Kharkiv, eastern Ukraine, for the past 60 years.

An ammonia leak at a chemical plant in the eastern Ukrainian city of Sumy has contaminated an area with a radius of more than 2.5 kilometers, officials said early Monday.

Sumy regional governor Dmytro Zhyvytskyy didn't say what caused the leak. The Sumykhimprom plant is on the eastern outskirts of the city, which has a population of about 263,000 and has been regularly shelled by Russian troops in recent weeks.

"For the center of Sumy, there is no threat now, since the wind does not blow on the city," said Zhyvytskyy, adding the nearby village of Novoselytsya, about 1.5 kilometers southeast of Sumy, is under threat. Emergency crews were working to contain the leak.

The U.N. has confirmed 902 civilian deaths in the war but concedes the actual toll is likely much higher. It says nearly 3.4 million people have fled Ukraine. Estimates of Russian deaths vary, but even conservative figures are in the low thousands. The Ukrainian prosecutor general's office says at least 115 children have been killed and 148 injured so far.

Some Russians also have fled their country amid a widespread crackdown on dissent. Russia has arrested thousands of anti-war protesters, muzzled independent media and cut access to social media sites like Facebook and Twitter.

International efforts

European Union governments will take up the discussion among foreign ministers on Monday, before U.S. President Joe Biden arrives in Brussels on Thursday for summits with NATO's 30 allies, as well as the EU and in a G-7 format including Japan. Diplomats told Reuters that Baltic countries including Lithuania are pushing for an embargo as the next logical step, while Germany is warning against acting too quickly because of already high energy prices in Europe.

In his latest appeal for help from abroad, Zelenskyy addressed the Israeli Knesset by video link on Sunday and questioned Israel's reluctance to sell its Iron Dome missile defense system to Ukraine.

"Everybody knows that your missile defense systems are the best ... and that you can definitely help our people, save the lives of Ukrainians, of Ukrainian Jews," said Zelenskyy, according to Reuters. He also welcomed the mediation efforts of Israeli Prime Minister Naftali Bennett, who has held numerous calls with him and Putin. He said in his daily video address to Ukrainians that "sooner or later we will begin to have talks with Russia, possibly in Jerusalem."

Meanwhile, Biden has added a stop in Poland to his trip this week to Europe. Poland is a crucial ally in the Ukraine crisis. It is hosting thousands of American troops and is taking in more people fleeing the war in Ukraine – more than 2 million – than any other nation in the midst of the largest European refugee crisis in decades.

Biden will head to Warsaw for a bilateral meeting with President Andrzej Duda scheduled for Saturday. He will discuss how the U.S., along with its allies and partners, is responding to "the humanitarian and human rights crisis that Russia's unjustified and unprovoked war on Ukraine has created," Psaki said.

Poland has been one of the most vocal countries in asking fellow NATO members to consider getting more involved to rein in the bloodshed.

Biden and NATO have said repeatedly that while the U.S. and NATO will provide weapons and other defensive support to non-NATO member Ukraine, they are determined to avoid any escalation on behalf of Kyiv that risks a broader war with Russia.

The Pentagon on March 9 rejected a Polish proposal for providing Ukraine with MiG fighter jets via a NATO air base, saying allied efforts against the Russian invasion should focus on more useful weaponry and that the MiG transfer with a U.S. and NATO connection would run a "high risk" of escalating the war.

Zelenskyy, has pleaded for the U.S. to provide his military with more aircraft and advanced air-defense systems. NATO and the United States have rejected his appeals to establish a "no-fly zone" over Ukraine to suppress Russian air power, saying it would put Western forces in direct conflict with Russian ones.

After Biden rallied European allies to join in sweeping sanctions against Russia over the invasion at the outset, his tasks now include dealing with some NATO members that are pushing for more involvement directly in the fighting. That includes proposals by Poland for peacekeepers.