Russian President Vladimir Putin ordered his military command to put nuclear-armed forces on high alert as Ukrainian fighters defending the city of Kharkiv said they had repelled an attack by invading Russian 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.
Putin's order is part of a pattern of Moscow manufacturing threats to justify aggression, White House Press Secretary Jen Psaki said on Sunday.
"We've seen him do this time and time again. At no point has Russia been under threat from NATO, has Russia been under threat from Ukraine," Psaki said on ABC's "This Week" program.
"This is all a pattern from President Putin and we're going to stand up to it. We have the ability to defend ourselves, but we also need to call out what we're seeing here from President Putin," Psaki added.
Russian soldiers and armoured vehicles have rolled into Kharkiv, Ukraine's second largest city, and witnesses reported firing and explosions. A natural gas pipeline was blown up before daybreak, a Ukrainian state agency said.
But city authorities said Ukrainian fighters had repelled the attack.
"Control over Kharkiv is completely ours! The armed forces, the police, and the defence forces are working, and the city is being completely cleansed of the enemy," regional Governor Oleh Sinegubov said.
Reuters was unable to immediately corroborate the information.
Ukrainian forces were also holding off Russian troops advancing on Kyiv.
"We have withstood and are successfully repelling enemy attacks. The fighting goes on," Zelenskiy said in a video message from the streets of Kyiv.
Australian Associated Press
Sign up for our newsletter to stay up to date.