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, forced hundreds and thousands of Ukrainians to flee west and could, according to the EU, eventually displace up to 7 million people.
Russia has become an international pariah as its forces do battle on the streets of Ukraine's cities, facing a barrage of sanctions including a ban 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 that 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 United States, 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.
Germany said Putin's nuclear manoeuvring was because the offensive had "halted" and was not going to plan.
The UN General Assembly will hold a rare emergency session Monday to discuss the conflict.
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 the country.
EU member states closed their airspace to Russian planes and many pledged arms for Ukraine -- but stressed they would not themselves intervene militarily.
British energy giant BP announced Sunday 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 provide 450 million euros ($500 million) for Ukraine to buy weapons and ban Russian central bank transactions, as well as restricting two Moscow-run media outlets.
Refugees from the conflict continued to stream into Ukraine's neighbours as Kyiv went to the International Court of Justice to accuse Russia of planning genocide.
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".
Crossing Medyka with his family, Ajmal Rahmani, an Afghan who fled Afghanistan for Ukraine four months before the US withdrawal, told AFP "I run from one war, come to another country and another war starts. Very bad luck".
Beers to bombs
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.
A regional official, Oleg Sinegubov, said Kharkiv had been brought under Ukrainian control and the army was expelling Russian forces.
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 a gas pipeline in eastern Kharkiv and an oil depot near the capital Kyiv had been targeted by Russian forces overnight Saturday to Sunday.
They said they were fighting off Russian forces in several other areas, and that 4,300 Russian troops had been killed.
Social media videos have shown what appear to be many Russian corpses, but 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 and the city is under a blanket curfew until Monday morning.
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 opposition 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".
Ukraine has called on its own civilians to fight Russia, with a brewery in Lviv in the country's west switching its production line from beers to bombs, making Molotov cocktails for the volunteer fighters.
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 the country'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.
In response to hostilities, FIFA ordered Russia to play its home international fixtures in neutral venues and warned it was considering banning it from the 2022 World Cup.
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.