Ukrainian officials have defiantly rejected a Russian demand that their forces in Mariupol lay down arms and raise white flags in exchange for safe passage out of the besieged strategic port city.
Even as Russia intensified its attempts to bombard Mariupol into surrender, its offensive in other parts of Ukraine has floundered.
Western governments and analysts see the broader conflict grinding into a war of attrition, with Russia continuing to barrage cities.
In the capital Kyiv, Russian shelling devastated a shopping centre near the city centre, killing at least eight people and leaving a sea of rubble amid scarred high-rises.
Ukrainian authorities also said Russia shelled a chemical plant in north-eastern Ukraine, causing an ammonia leak, 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.
Strikes hit an art school sheltering some 400 people only hours before Russia’s offer to open two corridors out of the city in return for the capitulation of its defenders, according to Ukrainian officials.
Ukrainian officials rejected the Russian proposal for safe passage out of Mariupol even before Russia’s deadline of 5am Moscow time (0200 GMT) 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 did not need to wait until the morning deadline to respond and cursing at the Russians, according to the news agency Interfax Ukraine.
Russian Colonel General Mikhail Mizintsev had offered two corridors – one heading east towards 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 Defence 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.
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.
Mariupol officials said at least 2,300 people have died in the siege, with some buried in mass graves.
Ahead of the rejected surrender offer, a Russian air strike hit the school where some 400 civilians were taking shelter and it was not clear how many casualties there were, Ukraine’s President Volodymyr Zelensky said in a video address early on Monday.
“They are under the rubble, and we don’t know how many of them have survived,” he said.
Mr Zelensky said Ukraine would “shoot down the pilot who dropped that bomb”.
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 theatre where more than 1,000 people were believed to be sheltering.
At least 130 people were reported rescued on Friday, but there has been no update since then.
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.
In the Black Sea port city of Odesa, authorities said Russian forces damaged civilian houses in a strike on Monday.
The city council said no-one was killed.
Some who were able to flee Mariupol tearfully hugged relatives as they arrived by train on Sunday in Lviv, about 1,100 kilometres (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.”
The fall of Mariupol 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 street 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.
US defence 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,” Mr Austin told CBS.
Talks between Russia and Ukraine have continued 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.
Mr Zelensky has said he would be prepared to meet Mr Putin in person, but Kremlin spokesman Dmitry Peskov said on Monday that more progress must be made first.
He said that “so far significant movement has not been achieved” in the talks.
Ukrainian delegation member Davyd Arakhamia told Ukrainska Pravda that there was a 90-minute session between top negotiators on Monday morning, to be followed by a full day of talks in various working groups.
US President Joe Biden was expected to talk later on 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.
The Russian Foreign Ministry warned that relations with the US are “on the verge of a breach” and summoned the US ambassador for an official protest, citing “unacceptable statements” by Mr Biden about Mr Putin – an apparent reference to the American calling the Russian a “war criminal”.
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 3am on 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.
Mr Konashenkov also said an overnight cruise missile strike hit a military training centre 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 centre there early on Monday but offered no details about injuries or deaths.
In Kyiv, eight people were killed by shelling in the densely populated Podil district not far from the city centre on Sunday, emergency officials said.
It devastated a shopping centre, leaving a flattened ruin still smouldering on 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.
Britain’s Ministry of Defence said on Monday that Ukrainian resistance had kept the bulk of Russian forces more than 25 kilometres (15 miles) from the city centre, but that Kyiv “remains Russia’s primary military objective”.
Russian troops are shelling Kyiv for a fourth week now and are trying to surround the capital, which had nearly three million people before the war.
Kyiv mayor Vitali Klitschko announced a curfew in the capital from Monday evening to 7am local time on Wednesday, telling residents to stay at home or in shelters.
A cluster of villages on Kyiv’s north-west 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.
In another worrying development, Ukraine’s nuclear regulatory agency said radiation monitors around the Chernobyl nuclear power plant, site of the world’s worst meltdown in 1986, have stopped working.
The agency said that, and a lack of firefighters to protect the area’s radiation-tainted forests as the weather warms, could mean a “significant deterioration” in the ability to control the spread of radiation in Ukraine and beyond.
Concerns have been expressed for safety at the shuttered plant since it was seized by Russian forces on February 24, the first day of the invasion.
Management at the plant said on Sunday that 50 staff members who had been working non-stop since the Russian takeover have been rotated out and replaced.
Earlier this month Russia shelled the working Zaporizhzhia nuclear plant, though no radiation was released.
