Russia demanded that Ukrainians in the besieged city of Mariupol lay down their arms Monday in exchange for safe passage out of town, but Ukraine rejected the offer. The Russian demand came hours after Ukrainian authorities said Moscow’s forces bombed an art school that was sheltering about 400 people. Russian forces would allow two corridors out of the coastal city, heading either east toward Russia or west to other parts of Ukraine, the Russian news agency TASS reported. It cited a statement from Colonel-General Mikhail Mizintsev, head of the Russian National Defense Control Center. TASS reported that Mariupol residents had been given until 5 a.m. Monday to respond to the offer. But Ukrainian Deputy Prime Minister Irina Vereshchuk rejected the notion. “There can be no talk of any surrender, laying down of arms. We have already informed the Russian side about this,” she told the news outlet Ukrainian Pravda. “I wrote: `Instead of wasting time on eight pages of letters, just open the corridor." Previous bids to allow residents to evacuate Mariupol and other Ukrainian cities have failed or have been only partially successful, with bombardments continuing as civilians sought to flee. Earlier Sunday, Ukrainian authorities said Russia's military bombed an art school in Mariupol, and tearful evacuees from the devastated port city described how “battles took place over every street,” weeks into the siege. The fall of Mariupol would allow Russian forces in southern and eastern Ukraine to link up. 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. Three weeks into the invasion, Western governments and analysts see the conflict shifting to a war of attrition, 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 their supply lines.