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.

Russia has been barraging the encircled southern city on the Sea of Azov, 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 continued to be 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 Irina 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."

U.S. President Joe Biden was expected to talk later Monday with the leaders of France, Germany, Italy and Britain to discuss the war, before heading later in the week to Brussels and then Poland for in-person talks.

Zelenskyy has been pleading with the U.S. for more aircraft and advanced air-defense systems, while NATO members on the alliance's eastern flank have also been looking for missile defense systems from the U.S. and Britain.

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 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, six 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.

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 antiwar protesters, muzzled independent media and cut access to social media sites like Facebook and Twitter.

From The Associated Press