A theatre in Mariupol where hundreds of people are reported to have been sheltering has been bombed by Russian forces, local officials have said.
The city council said the number of casualties was not yet known, but Sky News has verified footage from the attack as showing the Donetsk Regional Drama Theatre.
Earlier, Russian forces shot and killed 10 people queuing for bread in Chernihiv, northern Ukraine, the US embassy in Kyiv has said.
In a post on its Twitter account, the embassy wrote: “Such horrific attacks must stop.
“We are considering all available options to ensure accountability for any atrocity crimes in Ukraine.”
Putin lashes out at West, but hopes over peace talks grow – live updates
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Earlier, Ukrainian presidential adviser Mykhailo Podolyak said a “radical change” had occurred between Ukrainian and Russian forces after Kyiv launched counteroffensives in “several operational areas”.
It has substantially altered the “parties’ dispositions”, he tweeted, without elaborating further.
Another presidential adviser, Oleksiy Arestovych, said Ukrainian forces were conducting small-scale counter attacks on several fronts.
The situation in the “main hotspots has not changed”, he said, and “has no chance of changing as Russia has used up its resources”.
Russian troops are continuing to fire missiles at Ukrainian targets, and approximately two-thirds of rockets are hitting civilian buildings and infrastructure, Mr Arestovych claimed in a video briefing.
The UK Ministry of Defence, meanwhile, has said Ukraine is “adeptly exploiting” Russian forces’ “lack of manoeuvre” and inflicting heavy losses.
Moscow is also struggling to overcome “challenges” imposed by Ukraine’s terrain, it added.
High-rise buildings were again hit in Kyiv on Wednesday, however, and Russian troops are said to be shooting from inside a hospital in Mariupol, where about 500 people are being used as human shields.
In an update on Wednesday lunchtime, President Volodymyr Zelenskyy said Russian troops “continued to shell peaceful Ukrainian cities and towns” on Tuesday night, including Kharkiv and Kharkiv Oblast (province).
They also shelled the coast outside the southern port of Odesa, he added.
And in Bucha, in Kyiv province, six people from the town council were taken hostage, he said.
“The Russian state has turned into a real terrorist and it has no shame,” Mr Zelenskyy said.
Around Kyiv, though, Russia is still struggling to gather forces and is having problems with its people and logistics, General Sir Richard Barrons told Sky News.
Russian forces “doubt their ability to successfully fight for Kyiv other than demolishing it”, the retired British Army officer added – explaining why Moscow has stepped up its shelling of the capital.
But while Ukrainian forces are doing “really well”, they still do not have the capability to remove the Russians completely, he said.
General Sir Richard expects to see a “bigger attempt on Kyiv” soon, and it could be highly destructive.
In other developments:
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The MOD, in its latest intelligence update, said Russian troops have remained largely on the road network and have “demonstrated a reluctance to conduct off-road manoeuvre”.
The destruction of bridges by Ukrainian forces has also played a “key role in stalling Russia’s advance”.
The ministry continued: “Russia’s continued failure to gain control of the air has drastically limited their ability to effectively use air manoeuvre, further limiting their options.
“The tactics of the Ukrainian armed forces have adeptly exploited Russia’s lack of manoeuvre, frustrating the Russian advance and inflicting heavy losses on the invading forces.”
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A plume of smoke was seen rising into the sky after an artillery shell rammed into an apartment block in the centre of Kyiv on Wednesday morning, obliterating the top floor and starting a fire.
Two people were hurt, according to early reports.
In addition, social media footage shows two high-rise buildings in the capital’s Schevchenkivskyi district being shelled on Wednesday morning.
Loud booms are heard and smoke rises as the airstrikes hit. Sky News has verified the video and located it.
In Mariupol, Russian forces are shooting from artillery positions in the grounds of a hospital they captured on Tuesday, Ukrainian Deputy Prime Minister Iryna Vereshchuk said.
She added that 400 civilians, patients and medical staff are being held hostage.
Regional leader Pavlo Kyrylenko put that number at 500, saying troops had forced about 400 people from nearby homes into the Regional Intensive Care Hospital and about 100 patients and staff were not being allowed to leave.
President Zelenskyy said the “occupiers are using it as a shelling position” and it is a “war crime”.
A team of investigators from the International Criminal Court is in Ukraine collecting evidence, he added.
Ms Vereshchuk said it was an “open question” whether a humanitarian corridor would be opened in the port city on Wednesday.
Ukraine’s prosecutor general has said 103 children have now been killed since the invasion began.
Russian forces have struck more than 400 educational establishments and 59 of them have been destroyed, Iryna Venediktova said on Facebook.