The US said Putin was escalating the war with “dangerous rhetoric”, amid signs the biggest assault on a European state since World War Two was not producing rapid victories, but instead generating a far-reaching and concerted Western response.

The Ukrainian president’s office said negotiations with Moscow would be held at the Belarusian-Ukrainian border. It was not clear when they would start.

“I do not really believe in the outcome of this meeting, but let them try, so that later not a single citizen of Ukraine has any doubt that I, as president, tried to stop the war,” President Volodymyr Zelenskiy said.

Less than four days after it started, the invasion has triggered a Western political, strategic and economic response unprecedented in its extent and co-ordination.

The European Union decided for the first time in its history to supply weapons to a country at war.

As missiles fell on Ukrainian cities, nearly 400,000 civilians, mainly women and children, have fled into neighbouring countries. Hundreds were stranded in Kyiv on Sunday waiting for trains to take them away from the fighting.

The capital remained in Ukrainian government hands, with Zelenskiy rallying his people daily despite Russian shelling of civilian infrastructure.

The EU shut all Russian planes out of its airspace, as did Canada, while British oil giant BP announced it would give up its 19.75 per cent stake in Russia’s Rosneft, writing off up to $US25 billion ($A35 billion).

Putin, who has called the invasion a “special operation”, thrust an alarming new element into play when he ordered Russia’s “deterrence forces” – which wield nuclear weapons – onto high alert.

Putin had previously referred to his nuclear arsenal in a speech announcing the start of the invasion on Thursday, saying Russia’s response to any country that stood in its way would be immediate and carry “consequences that you have never encountered in your history”.

The EU foreign policy chief said Russia had clearly threatened a nuclear attack on countries supporting Ukraine after the invasion.

“Just to mention the possibility of using nuclear weapons – it’s such a gigantic irresponsibility that says a lot about the personality of (the person) who is doing that,” Josep Borrell told a news conference in Brussels.

“We are afraid that Russia is not going to stop in Ukraine.”

In the strongest economic sanctions yet, the United States and Europe said on Saturday they would banish big Russian banks from the main global payments system SWIFT and announced other measures to limit Moscow’s use of a $US630 billion ($A878 billion) war chest.

In New York, the UN Security Council convened a rare emergency meeting of its General Assembly of all 193 member states, for Monday.

A Ukrainian state news agency said Russian troops had blown up a natural gas pipeline in Kharkiv, Ukraine’s second-largest city, sending a burning cloud into the sky.

Soon after, Russian armour rolled into Kharkiv and witnesses reported firing and explosions. City authorities said the attack had been repelled.

Reuters was unable to corroborate the information.

Ukrainian forces also appeared to be holding off Russian troops advancing on Kyiv.

However, satellite imagery released by the private Maxar Technologies taken on Sunday showed a 5km-long convoy of Russian ground forces approximately 64km away heading towards Kyiv. The images could not be independently verified.

“We have withstood and are successfully repelling enemy attacks. The fighting goes on,” Zelenskiy said in the latest of several video messages from the streets of Kyiv.

A UN relief agency said more than 368,000 refugees had crossed into neighbouring countries, clogging railways, roads and borders.

At least 352 civilians, including 14 children, have been killed and 1684 people have been wounded, Ukraine’s Health Ministry said.

“The Russian army does not threaten civilians in Ukraine. It is not shelling civilian infrastructure,” Russian Ambassador Vassily Nebenzia told the UN Security Council.