Russian President Vladimir Putin ordered his military command to put nuclear-armed forces on high alert on Sunday as Ukrainian fighters defending the city of Kharkiv said they had repelled an attack by invading troops.
US Ambassador to the United Nations Linda Thomas-Greenfield said that "President Putin is continuing to escalate this war in a manner that is totally unacceptable and we have to continue to stem his actions in the strongest possible way".
On the fourth day of the biggest assault on a European state since World War Two, the Ukrainian president's office said negotiations between Kyiv and Moscow would be held at the Belarusian-Ukrainian border.
They would meet without preconditions, it said.
Thousands of Ukrainian civilians, mainly women and children, were fleeing from the Russian assault into neighbouring countries.
The capital Kyiv was still in Ukrainian government hands, with President Volodymyr Zelenskiy rallying his people despite Russian shelling of civilian infrastructure.
But Putin, who has described the invasion as a "special military operation", thrust an alarming new element into play on Sunday when he ordered Russia's deterrence forces - a reference to units which include nuclear arms - onto high alert.
He cited aggressive statements by NATO leaders and economic sanctions imposed by the West against Moscow.
"As you can see, not only do Western countries take unfriendly measures against our country in the economic dimension - I mean the illegal sanctions that everyone knows about very well - but also the top officials of leading NATO countries allow themselves to make aggressive statements with regards to our country," Putin said on state television.
Russian soldiers and armoured vehicles rolled into Kharkiv, Ukraine's second largest city, and witnesses reported firing and explosions.
But city authorities said Ukrainian fighters had repelled the attack.
In other developments, Russian troops blew up a natural gas pipeline in Kharkiv before daybreak, a Ukrainian state agency said, sending a burning cloud up into the darkness.
Ukraine's Western allies ratcheted up their response to Russia's land, sea and air invasion with an almost blanket ban on Russian airlines using European airspace.
In the strongest economic sanctions yet on Moscow, the United States and Europe said on Saturday they would banish big Russian banks from the main global payments system and announced other measures aimed at limiting Moscow's use of a $630 billion war chest of central bank reserves.
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