LVIV, Ukraine — 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.

Even as Russia intensified its attempt to pummel Mariupol into surrender, its offensive in other parts of Ukraine has floundered. Western governments and analysts say the broader conflict is grinding into a war of attrition, with Russia continuing to bombard cities.

In the capital, Kyiv, a shopping center in the densely populated Podil district near the city center was a smoldering, flattened ruin Monday after being hit the day before by shelling that killed eight people, according to emergency officials. The force of the explosion shattered every window in a neighboring high-rise. Artillery boomed in the distance as firefighters picked their way through the destruction.

Ukrainian authorities also said Russia shelled a chemical plant in northeastern Ukraine, sending toxic ammonia leaking into the air, and hit a military training base in the west with cruise missiles.

The encircled southern city of Mariupol on the Sea of Azov has seen some of the worst horrors of the war, under Russian pounding for more than three weeks, in a brutal assault that Ukrainian and Western officials have called a war crime.

Strikes hit an art school sheltering some 400 people only hours before Russia’s offer to open corridors out of the city in return for the capitulation of its defenders, according to Ukrainian officials.

Ukraine’s President Volodymyr Zelenskyy said it was not clear how many casualties there were.

“They are under the rubble, and we don’t know how many of them have survived,” he said in a video address, vowing that Ukraine would “shoot down the pilot who dropped that bomb.”

Russian Col. Gen. Mikhail Mizintsev had offered two corridors — one heading east toward Russia and the other west to other parts of Ukraine — in return for Mariupol’s surrender. 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.

Ukrainian officials rejected the proposal even before Russia’s deadline of 5 a.m. Moscow time (0200GMT) 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 quickly dismissed the offer, 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.

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. At least 130 people were reported rescued Friday, but there has been no update since then.

Mariupol officials said at least 2,300 people have died in the siege, with some buried in mass graves.

City officials and aid groups say Russian bombardment has cut off Mariupol’s electricity, water and food supplies and severed its communications with the outside world, plunging the remaining residents into a chaotic fight for survival.

“What’s happening in Mariupol is a massive war crime,” EU foreign policy chief Josep Borrell said Monday.

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

Some who were able to escape Mariupol tearfully hugged relatives as they arrived by train Sunday in Lviv in western Ukraine.

“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.”

Mariupol is a key Russian target because its fall would allow Russian forces in southern and eastern Ukraine to unite. But Western military analysts say that even if the 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.

More than three weeks into the invasion, the two sides now seem to be trying to wear each other down, 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.

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.

Talks between Russia and Ukraine have continued by video conference but failed to bridge the chasm between the two sides, with Russia demanding Ukraine disarm and Ukraine saying Russian forces must withdraw from the whole country.

Zelenskyy has said he would be prepared to meet Putin in person, but Kremlin spokesman Dmitry Peskov said Monday that more progress must be made first. He said that “so far significant movement has not been achieved” in the talks.

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.

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

Ukraine’s prosecutor general said a Russian shell struck a chemical plant outside the eastern city of Sumy just after 3 a.m. Monday, causing a leak in a 50-ton tank of ammonia that took hours to contain.

Russian military spokesman Igor Konashenkov claimed the leak was a “planned provocation” by Ukrainian forces to falsely accuse Russia of a chemical attack.

Konashenkov also said an overnight cruise missile strike hit a military training center in the Rivne region of western Ukraine. He said 80 foreign and Ukrainian troops were killed, though the figure could not be independently confirmed. Vitaliy Koval, the head of the Rivne regional military administration, confirmed a twin Russian missile strike on a training center there early Monday but offered no details about injuries or deaths.

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. Kyiv Mayor Vitali Klitschko announced a curfew in the capital from Monday evening to 7 a.m. local time Wednesday, telling residents to stay at home or in shelters.

A cluster of villages on Kyiv’s northwest edge, including Irpin and Bucha, have been all but cut off by Russian forces and are on the verge of humanitarian catastrophe, regional officials said. Associated Press journalists who were in the area a week ago saw bodies in a public park, and not a day goes by without smoke rising from the area.

Britain’s defense ministry said Monday that Ukrainian resistance had kept the bulk of Russian forces more than 25 kilometers (15 miles) from the city center, but that Kyiv “remains Russia’s primary military objective.”

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.