Russian forces have launched co-ordinated missile and artillery attacks on Ukrainian cities, including the capital, Kyiv, where gunfire erupted near government buildings in the city centre, military officials say.
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Ukrainian authorities have urged citizens to help defend Kyiv from advancing Russian forces who invaded on Thursday in the worst European security crisis in decades.
But even as the fighting grew more intense, the Russian and Ukrainian governments signalled an openness to negotiations, offering the first glimmer of hope for diplomacy since Russian President Vladimir Putin launched the invasion.
Artillery shells exploded in Kyiv, a witness said.
Ukrainian officials said Russian forces fired cruise missiles from the Black Sea at the cities of Sumy, Poltava and Mariupol.
There was also heavy fighting near the southern city of Mariupol, they said.
"The fate of Ukraine is being decided right now," President Volodymyr Zelenskiy said on Friday in a video address posted to his Telegram channel.
The air force command earlier reported heavy fighting near an air base at Vasylkiv, southwest of the capital, which it said was under attack from Russian paratroopers.
It said one of its fighters had shot down a Russian transport plane. Reuters could not independently verify the claims.
Mykhailo Podolyak, adviser to the president's office, said the situation in Kyiv and its outskirts was under control.
"There are cases of sabotage and reconnaissance groups working in the city, police and self-defence forces are working efficiently against them," Podolyak said.
Kyiv residents were urged by the defence ministry to make petrol bombs to repel the invaders.
Some families cowered in shelters and hundreds of thousands have left their homes to find safety, according to a UN aid official.
Ukraine said more than 1000 Russian soldiers had been killed. Russia did not release casualty figures. Zelenskiy said late on Thursday 137 soldiers and civilians been killed with hundreds wounded.
After weeks of warnings from Western leaders, Putin unleashed a three-pronged invasion of Ukraine from the north, east and south on Thursday, in an attack that threatened to upend Europe's post-Cold War order.
"I once again appeal to the military personnel of the armed forces of Ukraine: do not allow neo-Nazis and (Ukrainian radical nationalists) to use your children, wives and elders as human shields," Putin said at a televised meeting with Russia's Security Council.
"Take power into your own hands."
Putin has cited the need to "denazify" Ukraine's leadership as one of his main reasons for invasion, accusing it of genocide against Russian-speakers in eastern Ukraine.
Kyiv and its Western allies dismiss the accusations as baseless propaganda.
Ukrainians voted overwhelmingly for independence in 1991 at the fall of the Soviet Union and Kyiv is hoping to join NATO and the EU - aspirations that infuriate Moscow.
Putin says Ukraine, a democratic nation of 44 million people, is an illegitimate state carved out of Russia, a view Ukrainians see as aimed at erasing their more than thousand-year history.
Western countries have announced a barrage of sanctions against Russia, including blacklisting its banks and banning technology exports. But they have stopped short of forcing it out of the SWIFT system for international bank payments.
The United States imposed sanctions on Putin, Foreign Minister Sergei Lavrov, Defence Minister Sergei Shoigu and Chief of General Staff Valery Gerasimov. The European Union and Britain earlier froze any assets Putin and Lavrov held in their territory. Canada took similar steps.
But amid the chaos of war came a ray of hope.
A spokesman for Zelenskiy said Ukraine and Russia would consult in coming hours on a time and place for talks.
The Kremlin said earlier it offered to meet in the Belarusian capital Minsk after Ukraine expressed a willingness to discuss declaring itself a neutral country while Ukraine had proposed Warsaw as the venue.
That, according to Russian spokesman Dmitry Peskov, resulted in a "pause" in contacts.
"Ukraine was and remains ready to talk about a ceasefire and peace," Zelenskiy's spokesman, Sergii Nykyforov, said in a Facebook post.
"We agreed to the proposal of the President of the Russian Federation."
But US State Department spokesman Ned Price said Russia's offer was an attempt to conduct diplomacy "at the barrel of a gun" and Putin's military must stop bombing Ukraine if it is serious about negotiations.
At the United Nations, Russia vetoed a draft Security Council resolution that would have deplored its invasion, while China abstained, which Western countries took as proof of Russia's isolation.
The United Arab Emirates and India also abstained while the remaining 11 members voted in favour.
The White House asked Congress for $US6.4 billion in security and humanitarian aid for the crisis, officials said, and President Biden instructed the US State Department to release $US350 million in military aid.