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 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.

The meeting is set to take place near Chernobyl — the site of the world's worst nuclear disaster.

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.

“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.

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 lodges case against Russia in The Hague

Ukraine also lodged a complaint against Russia at the International Court of Justice (ICJ) in The Hague to get it to halt its invasion.

Russia must be held accountable for manipulating the notion of genocide to justify aggression," Zelensky declared in a tweet.

"We request an urgent decision ordering Russia to cease military activity now and expect trials to start next week."

The ICJ, which is based in the Netherlands capital The Hague, does not have a mandate to bring criminal charges against individual Russian leaders behind the four-day-old invasion.

But it is the world's top court for resolving legal complaints between states over alleged breaches of international law. It is the supreme judicial institution of the United Nations.

Banking curbs on Russia

The US, European Union and the United Kingdom agreed to block “selected” Russian banks from the SWIFT global financial messaging system, which moves money around more than 11,000 banks and other financial institutions worldwide, part of a new round of sanctions aiming to impose a severe cost on Moscow for the invasion.

They also agreed to impose ”restrictive measures” on Russia’s central bank.

It was unclear how much territory Russian forces had seized or to what extent their advance had been stalled. Britain’s Ministry of Defense said, “the speed of the Russian advance has temporarily slowed likely as a result of acute logistical difficulties and strong Ukrainian resistance.”

A senior US defence official said more than half the Russian combat power that was massed along Ukraine’s borders had entered the country and Moscow has had to commit more fuel supply and other support units inside Ukraine than originally anticipated.

The official spoke on the condition of anonymity to discuss internal US assessments.

The curfew forcing everyone in Kyiv inside was set to last through Monday morning. The relative quiet of the capital was sporadically broken by gunfire.

Fighting on the city’s outskirts suggested that small Russian units were trying to clear a path for the main forces. Small groups of Russian troops were reported inside Kyiv, but Britain and the US said the bulk of the forces were 30 kilometres from the city’s centre as of Saturday afternoon.

Russia claims its assault on Ukraine from the north, east and south is aimed only at military targets, but bridges, schools and residential neighbourhoods have been hit.

Ukraine’s health minister reported on Saturday that 198 people, including three children, had been killed and more than 1,000 others wounded during Europe’s largest land war since World War II. It was unclear whether those figures included both military and civilian casualties.

A missile struck a high-rise apartment building in Kyiv’s southwestern outskirts near one of the city’s two passenger airports, leaving a jagged hole of ravaged apartments over several floors. A rescue worker said six civilians were injured.

200 Russian soldiers captured

Ukraine’s ambassador to the US, Oksana Markarova, said troops in Kyiv were fighting Russian “sabotage groups.” Ukraine says some 200 Russian soldiers have been captured and thousands killed.

Markarova said Ukraine was gathering evidence of shelling of residential areas, kindergartens and hospitals to submit to The Hague as possible crimes against humanity.

Zelenskyy reiterated his openness to talks with Russia in a video message, saying he welcomed an offer from Turkey and Azerbaijan to organize diplomatic efforts, which so far have faltered.

The Kremlin confirmed a phone call between Putin and Azerbaijani President Ilham Aliyev but gave no hint of restarting talks.

A day earlier, Zelenskyy offered to negotiate a key Russian demand: abandoning ambitions of joining Nato.

Putin sent troops into Ukraine after denying for weeks that he intended to do so, all the while building up a force of almost 200,000 troops along the countries’ borders.

He claims the West has failed to take seriously Russia’s security concerns about Nato, the Western military alliance that Ukraine aspires to join. But he has also expressed scorn about Ukraine’s right to exist as an independent state.

The effort was already coming at great cost to Ukraine, and apparently to Russian forces as well.

Ukrainian artillery fire destroyed a Russian train delivering diesel to troops heading toward Kyiv from the east, said Anton Gerashchenko, an adviser to the interior minister.

The country’s Infrastructure Ministry said a Russian missile was shot down early on Saturday as it headed for the dam of the sprawling reservoir that serves Kyiv.

The government also said a Russian convoy was destroyed. Video images showed soldiers inspecting burned-out vehicles after Ukraine’s 101st brigade reported destroying a column of two light vehicles, two trucks and a tank. The claim could not be verified.

Highways into Kyiv from the east were dotted with checkpoints manned by Ukrainian troops and young men in civilian clothes carrying automatic rifles. Low-flying planes patrolled the skies, though it was unclear if they were Russian or Ukrainian.

In addition to Kyiv, the Russian assault appeared to focus on Ukraine’s economically vital coastal areas, from near the Black Sea port of Odesa in the west to beyond the Azov Sea port of Mariupol in the east.

Ukrainian soldiers in Mariupol guarded bridges and blocked people from the shoreline amid concerns the Russian navy could launch an assault from the sea.

“I don’t care anymore who wins and who doesn’t,” said Ruzanna Zubenko, whose large family was forced from their home outside Mariupol after it was badly damaged by shelling.

“The only important thing is for our children to be able to grow up smiling and not crying.”

Fighting also raged in two eastern territories controlled by pro-Russia separatists. Authorities in Donetsk said hot water supplies to the city of about 900,000 were suspended because of damage to the system by Ukrainian shelling.

Ukrainian president declines US offer

The US government urged Zelenskyy early on Saturday to evacuate Kyiv but he turned down the offer, according to a senior American intelligence official with direct knowledge of the conversation. Zelenskyy issued a defiant video recorded on a downtown street, saying he remained in the city.

“We aren’t going to lay down weapons. We will protect the country,” he said. “Our weapon is our truth, and our truth is that it’s our land, our country, our children. And we will defend all of that.”

Hungary and Poland both opened their borders to Ukrainians.

Refugees arriving in the Hungarian border town of Zahony said men between the ages of 18 and 60 were not being allowed to leave Ukraine.

“My son was not allowed to come. My heart is so sore, I’m shaking,” said Vilma Sugar, 68.

At Poland’s Medyka crossing, some said they had walked for 15 miles (35km) to reach the border.

“They didn’t have food, no tea, they were standing in the middle of a field, on the road, kids were freezing,” Iryna Wiklenko said as she waited on the Polish side for her grandchildren and daughter-in-law to make it across.

Officials in Kyiv urged residents to stay away from windows to avoid debris or bullets.

Shelves were sparsely stocked at grocery stores and pharmacies, and people worried how long food and medicine supplies might last.

The US and its allies have beefed up forces on Nato's eastern flank but so far have ruled out deploying troops to fight Russia. Instead, the US, the European Union and other countries have slapped wide-ranging sanctions on Russia, freezing the assets of businesses and individuals including Putin and his foreign minister.

Dmitry Medvedev, the deputy head of Russia’s Security Council, warned that Moscow could react by opting out of the last remaining nuclear arms pact, freezing Western assets and cutting diplomatic ties.

“There is no particular need in maintaining diplomatic relations,” Medvedev said. “We may look at each other in binoculars and gunsights.”