Ukrainian President Volodymyr Zelenskiy renewed his call for negotiations with Russian President Vladimir Putin, even as he and others accused Moscow of war crimes and as deadly street fighting raged in the key southern port city of Mariupol, where a major evacuation is set for March 21.
"I'm ready for negotiations with him," Zelenskiy told CNN in an interview on March 20 as Russia’s widely condemned, unprovoked invasion of Ukraine entered its fourth week.
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"I think without negotiations, we cannot end this war," Zelenskiy said through a translator.
"If there is just a 1 percent chance for us to stop this war, I think that we need to take this chance...to have the possibility of negotiating, the possibility of talking to Putin," he said.
"If these attempts fail, that would mean that this is a third world war."
Separately Turkey's foreign minister said in an interview that Russian and Ukrainian negotiators were nearing agreement on "critical" issues and that he was hopeful for a potential cease-fire soon in the conflict.
Foreign Minister Mevlut Cavusoglu earlier this month hosted talks between Russian Foreign Minister Sergei Lavrov and his Ukrainian counterpart, Dmytro Kuleba, in the Turkish city of Antalya, but those talks did not appear to yield concrete results.
As Zelenskiy spoke to CNN, fighting continued in Mariupol, a strategic city that had a population of 400,000 before the war broke out. Residents have for the past two weeks been trapped without basic supplies, such as water, food, and fuel.
Russia is seeking to take control of the city, which would allow it to link Crimea -- which it seized in 2014 -- with territory controlled by Kremlin-backed separatists in eastern Ukraine.
The Russian military said it had given Ukraine until the early hours of March 21 to surrender the city, according to Russian media.
But Ukrainian Deputy Prime Minister Iryna Vereshchuk said early on March 21 that "there can be no question of any surrender, laying down of arms. We have already informed the Russian side about this."
Zelenskiy and other Ukrainian officials accused Moscow of war crimes after the Russian military bombed a Mariupol art school where some 400 people had sought refuge from the intense fighting.
Local officials on March 20 said on their Telegram channel that the school’s building was destroyed and that people could remain under the rubble. There was no immediate word on casualties.
“To do this to a peaceful city -- what the occupiers did -- is a terror that will be remembered for centuries to come,” Zelenskiy said in a video address to the nation early on March 20.
The attack on the art school came after Russian air strikes on March 16 flattened a theater in Mariupol where civilians were sheltering. City authorities said 130 people were rescued but that many more could remain under the debris. Rescue workers were still searching for survivors.
Earlier in the war, Russian forces bombed a maternity hospital in the city.
Russia denies targeting civilians despite widespread evidence of deadly attacks on nonmilitary sites.
Late on March 20, Ukraine’s central government said it plans to send dozens of buses to Mariupol to aid the evacuation of refugees fleeing fighting there.
Deputy Prime Minister Vereshchuk said nearly 50 buses were set to arrive in the city on March 21.
She said that 3,985 people were evacuated on March 20 from Mariupol to the city of Zaporizhzhya about 225 kilometers away.
WATCH: Russian forces are meeting fierce resistance and taking casualties as they try to move towards the Ukrainian capital, Kyiv. On March 18, a Ukrainian special search group collected the dead bodies of Russian soldiers in the hope they could be exchanged for Ukrainian prisoners of war.
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Ukrainian Team Collects Dead Russian Soldiers To Exchange For Ukrainian POWs
While the Russian invasion has reportedly bogged down in much of the country and has resulted in heavy losses of troops and military equipment, Russian forces continue to bombard Ukrainian cities amid international condemnation and calls for an immediate cease-fire.
Observers have speculated that Russian military momentum has been stopped by Ukrainian forces in many parts of the country and that the sides could be heading for a long, protracted stalemate in the war, which began on February 24 with Russia’s invasion of its neighbor.
In the capital, Kyiv, Mayor Vitali Klitschko said late on March 20 that shelling had hit residential areas and a shopping district in the Podil district after a relatively quiet day.
"Several explosions in the capital's Podil district," Klitschko said on his Telegram channel.
Nearly one-fourth of Ukraine’s population has been displaced by the invasion, according to UN figures released on March 20.
Filippo Grandi, head of the UN refugee agency (UNHCR), said on Twitter that at least 10 million of Ukraine's population of 44 million people have fled their homes.
About 3.4 million have fled across Ukraine's borders to neighboring countries, with the bulk of them arriving in Poland, a member of NATO and the European Union.
The UN human rights office estimated on March 20 that 902 civilians have been killed and 1,459 injured in Ukraine as of the end of March 19. It said, though, that the actual toll is likely to be much higher as it has not been able to verify reports in several badly damaged cities.
The UN said most of the casualties were through shelling from heavy artillery and multiple-launch rocket systems, as well as missiles and air strikes.
When asked by British broadcaster Sky News if Russia was committing genocide in her country, Ukrainian Deputy Prime Minister Olha Stefanishyna said: "It's not a question. It's simply the reality we all face."
WATCH: Two-year-old Stepan Shpak was killed in Novye Petrivtsy, near the Ukrainian capital, Kyiv, on March 16 in shelling by the Russian Army. His father spoke to Current Time on March 17.
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Father Of Child Killed In Russian Shelling: 'What Is All This For? For What?'
Protests against Russia’s invasion continued in several cities around the world, including in Russia itself, despite police crackdowns on demonstrators.
Demonstrations took Moscow, St. Petersburg, Yekaterinburg, Nizhny Novgorod, and Vladivostok, among other cities, according to OVD-Info, an NGO that monitors arrests during protests.
Since the invasion began, there have been more than 15,000 detentions at anti-war protests, OVD-Info reported.
Military casualty figures on both sides remain difficult to confirm.
Zelenskiy said in a video message targeting the Russian public on March 20 that some 14,000 Russians have died in the invasion.
"That's 14,000 mothers, 14,000 fathers, wives, children, relatives, friends -- and you don't notice?" he said.
Moscow has only acknowledged 498 deaths, a total announced early in the invasion with no subsequent updates.
WATCH: Belarus has withdrawn all of its diplomats from Ukraine. When Ambassador Ihar Sokol was leaving on March 18, a Ukrainian border officer tried to hand him "30 pieces of silver" -- a reference to the biblical story of the betrayal of Jesus by Judas. Russian troops who were deployed in Belarus for military exercises joined the invasion of Ukraine, which began on February 24.
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Belarus's Ambassador Offered '30 Pieces Of Silver' As He Left Ukraine
Ukraine said a week ago that about 1,300 of its soldiers had been killed. That number cannot be independently confirmed.
Global condemnation of Russia's invasion continued, with Pope Francis calling it a "senseless massacre" and a "repugnant war."
However, Russian ally China has not joined in the criticism of Russia or participated in financial sanctions placed on Moscow.
British Prime Minister Boris Johnson urged Beijing to take a stand against the invasion.
"As time goes on, and as the number of Russian atrocities mounts up, I think it becomes steadily more difficult and politically embarrassing for people either actively or passively to condone Putin's invasion," he told The Times newspaper.
U.S. President Joe Biden is scheduled to travel in the upcoming week to Europe for emergency NATO talks on the Ukraine war.
Ukrainian officials have invited Biden to come to the country to see the situation for himself, but the White House said the president has no plans to visit the war-torn nation during this trip.
With reporting by AP, AFP, dpa, BBC, and Reuters