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Russian forces have seized control of a key port city in southern Ukraine, the mayor says.
Kherson is the first major city to be taken by Russia, after heavy fighting, since it invaded a week ago.
Its mayor, Igor Kolykhaev, said Russian troops had forced their way into the city council building and imposed a curfew on residents.
Several cities have come under intense shelling, with Wednesday one of the most destructive days of the fighting.
An investigation into possible war crimes and crimes against humanity committed in Ukraine has been launched by the International Criminal Court (ICC) in The Hague.
Russia has for the first time admitted taking heavy military casualties during its attack on Ukraine, with 498 troops killed and a further 1,597 injured. Ukraine says Russia's losses run into the thousands.
Ukraine reports that more than 2,000 civilians have died since the invasion began last Thursday. The conflict has also caused more than a million people to flee Ukraine, according to the UN.
In a Facebook post, Mr Kolykhaev said Russian forces were in control of Kherson, a port on Ukraine's southern Black Sea coast with a population of more than 280,000 people.
He urged Russian soldiers not to shoot at civilians, saying there were no Ukrainian forces in the city.
Mr Kolykhaev called on residents to follow conditions set by Russian forces in order to "keep the Ukrainian flag flying". These include:
"The (Russian) occupiers are in all parts of the city and are very dangerous," Gennady Lakhuta, head of the regional administration, was quoted as saying by AFP news agency.
The capture of Kherson - located on the banks of the Dnieper River where it flows into the Black Sea - is significant because it could allow Russia to create a base for the military there as it seeks to push further inland.
Ukraine's second-largest city, Kharkiv, came under a fierce aerial assault. Its mayor told the BBC shelling and cruise missile strikes were hitting residential areas and inflicting heavy civilian casualties.
And in the southern port of Mariupol, hundreds are feared dead following hours of sustained shelling.
But Russian efforts to encircle the capital Kyiv have slowed, with one US official saying a huge Russian convoy to the north of the city barely moved all day on Wednesday.
Large explosions were heard in the capital overnight into Thursday, with footage showing a huge fireball lighting up the night sky.
Four blasts were heard in the city centre, near Friendship of the Peoples metro station, Ukrainian media report.
In other developments:
Pictures of fighting in Ukraine have prompted international condemnation of Russia, with an overwhelming majority of UN countries calling on Moscow to immediately withdraw its troops.
Only five countries voted against the resolution, including Syria and North Korea.
The ICC said it was collecting evidence into possible violations after 39 countries called for it to open an inquiry.
They include the UK, with Prime Minister Boris Johnson personally accusing Russian President Vladimir Putin of committing "horrific" atrocities on Ukraine's cities.
Joel Gunter, BBC News, Ukraine
After more than 15 hours of continuous bombardment by Russian forces, the key Ukrainian port city of Mariupol is "near to a humanitarian catastrophe", the city's deputy mayor told the BBC.
"The Russian army is working through all their weapons here - artillery, multiple rocket launch systems, airplanes, tactical rockets. They are trying to destroy the city," Serhiy Orlov said.
Mr Orlov said Russian forces were several kilometres from the city on all sides and had launched strikes on key infrastructure, cutting water and power supplies to parts of the city. One densely populated residential district on the city's left bank had been "nearly totally destroyed", he said.
"We cannot count the number of victims there, but we believe at least hundreds of people are dead. We cannot go in to retrieve the bodies. My father lives there, I cannot reach him, I don't know if he is alive or dead."
Ukraine's army has resisted Russian forces so far in key parts of the country but the increased aerial bombardment of cities has raised fears Russia is shifting tactics.
"The Ukrainian army is very brave and they will continue to defend the city but the style of the Russian army is like pirates - they do not fight with their army, they just destroy entire districts," Mr Orlov said.
"We believe in our Ukrainian army, but we are in a terrible situation."
