Updated 8pm

Ukraine vowed not to give ground at talks with Moscow on Sunday as Ukrainian forces resisted a Russian invasion four days in and Moscow put its nuclear forces on high alert.

Fighting has claimed dozens of civilian lives and could, according to the EU, displace up to seven million people. 

Russia has become an international pariah as the forces do battle on the streets of Ukraine's cities, facing a barrage of sanctions and banned from Western airspace and key financial networks.

Ukraine said it had agreed to send a delegation to meet Russian representatives on the border with Belarus, which has allowed Russian troops passage to attack Ukraine.

But Kyiv insisted there were no pre-conditions to the talks.

"We will not capitulate, we will not give up a single inch of our territory," Ukrainian Foreign Minister Dmytro Kuleba said ahead of the first public contact between the two sides since war erupted.

Ukraine's President Volodymyr Zelensky was sceptical. 

"As always: I do not really believe in the outcome of this meeting, but let them try," he said.

Ukrainian forces said they had defeated a Russian incursion into Ukraine's second city Kharkiv, 500 kilometres (310 miles) east of Kyiv, on day four of an invasion which stunned the world.

As Western countries lined up to send arms to Ukraine and impose suffocating sanctions, Russian President Vladimir Putin ordered Russia's nuclear "deterrence forces" onto high alert.

The US, the world's second largest nuclear power, slammed Putin's order as "totally unacceptable" while Kuleba said the move would not break his country's resolve. 

'Brutal' night

Ukraine has reported 198 civilian deaths, including three children, since the invasion began and Russia acknowledged for the first time that a number of its forces had been killed or injured.

The UN has put the civilian toll at 64 while the EU said more than seven million people could be displaced by the conflict.

"We are witnessing what could become the largest humanitarian crisis on our European continent in many, many years," the EU commissioner for crisis management Janez Lenarcic said.

Zelensky, who has defied Russia's onslaught and rallied his country with determined appearances on social media, admitted: "The past night in Ukraine was brutal.

"They fight against everyone. They fight against all living things -- against kindergartens, against residential buildings and even against ambulances."

Russia, which has the world's largest stockpile of nuclear weapons, accused Western countries of taking "unfriendly" steps against his country.

EU member states closed their airspace to Russian planes on Sunday and many pledged arms for Ukraine -- but stressed they will not themselves intervene militarily. 

British energy giant BP announced Sunday that it was pulling its 19.75-percent stake in Rosneft, a blow to Russia's key oil and gas sector, which is partly reliant on Western technology. 

Brussels also announced it would fund weapons deliveries to Ukraine and ban Moscow-run media networks RT and Sputnik.

Refugees from the conflict continued to stream into Ukraine's neighbours.

At the Medyka border crossing with Poland, volunteer Jasinska said the long line of arrivals, mostly women and children, were "in need of warm jackets, hats, gloves, but also children's clothes".

Builder Igor, 45, from the Ukrainian city of Chernihiv said his two daughters had "already been waiting for 20 hours along with my wife to cross over into Poland".

Overnight clashes

Automatic gunfire and explosions were heard in Kharkiv earlier on Sunday and AFP saw the smouldering wreckage of a Russian armoured vehicle and several others abandoned.

"Kharkiv is fully under our control," the head of the regional administration, Oleg Sinegubov, said on Telegram, adding that the army was expelling Russian forces during a "clean-up" operation.

Moscow has made better progress in the south, however, and said it was besieging the cities of Kherson and Berdyansk.

Both are located close the Crimea peninsula, which Russia annexed from Ukraine in 2014, and from which it launched one of several invasion forces.

Ukrainian officials said that a gas pipeline in eastern Kharkiv and an oil depot near the capital Kyiv were targeted by Russian forces overnight.

Ukraine said it was fighting off Russian forces in several other areas, and that 4,300 Russian troops had been killed. 

Russia admitted for the firs time Sunday that some of its troops and been killed and injured, but did not say how many. Social media videos have shown many apparent Russian corpses.

None of the claims could be independently verified.

In Kyiv, many residents spent another night in shelters or cellars as Ukrainian forces said they were fighting off Russian "sabotage groups".

But Sunday was relatively calm compared to the first days of fighting.

The city is under a blanket curfew until Monday morning, though some residents ventured out regardless.

Out for a walk in a park, Flora Stepanova, 41, said staying at home watching the news "will drive you crazy".

On Saturday, Russia ordered its forces to advance further into Ukraine "from all directions" but its soldiers have encountered fierce resistance from Ukrainian troops.

Western sources said the intensity of the resistance had apparently caught Moscow by surprise.

On Sunday, Ukraine's military urged willing foreigners to travel to Ukraine "and fight side-by-side with Ukrainians against Russian war criminals".

Crippling bank sanctions

Escalating its punitive response, the West said it would remove some Russian banks from the SWIFT bank messaging system, and froze central bank assets -- hitting Russia's global trade.

A senior US official said a task force would hunt down Russian assets belonging to Russia's influential billionaires.

The NATO alliance condemned Putin's nuclear alert and has said it will, for the first time, deploy part of its rapid response force to the region to reassure eastern allies.

The Kremlin has so far brushed off sanctions, including those targeting Putin personally, as a sign of Western impotence.

Putin has said Russia's actions are justified because it is defending Moscow-backed separatists in eastern Ukraine.

The rebels have been fighting Ukrainian government forces for eight years in a conflict that has killed more than 14,000 people.