Ukraine said Sunday it had agreed to talks with Russia after four days of conflict, as Russian President Vladimir Putin ordered his defence chiefs to put nuclear "deterrence forces" on alert.
The conflict has already killed dozens of civilians, forced hundreds of thousands to flee.
President Volodymyr Zelensky's office said a Ukrainian delegation would meet the Russian one at the border with Belarus, which has allowed Russian troops passage to attack Ukraine. The meeting is set to take place near Chernobyl -- the site of the world's worst nuclear disaster.
"The politicians agreed that the Ukrainian delegation would meet the Russian one without preconditions," Zelensky's office said in a statement after the president spoke to his Belarusian counterpart Alexander Lukashenko. Ukrainian forces earlier said they had fought off a Russian incursion into Ukraine's second biggest city, Kharkiv, on day four of Russia's invasion.
As Western countries lined up to send arms into Ukraine and impose ever more stringent sanctions, Putin ordered his defence chiefs to put the country's nuclear "deterrence forces" on high alert.
Putin accused Western countries of taking "unfriendly" steps against his country. Ukraine has reported 198 civilian deaths, including three children, since the invasion began.
The UN has put the civilian toll at 64. "The past night in Ukraine was brutal," Zelensky said.
"They fight against everyone. They fight against all living things -- against kindergartens, against residential buildings and even against ambulances." Several European countries meanwhile banned Russian airlines from their airspace on Sunday and many pledged arms for Ukraine but made it clear that they will not intervene militarily.
In his traditional Sunday message to the faithful in St Peter's Square, Pope Francis called for weapons to "fall silent" in the country and for the opening of humanitarian corridors. A day after Berlin said it would send anti-tank weapons and Stinger missiles to Ukraine, German Chancellor Olaf Scholz said the world was in a "new era" and warned of further sanctions.
Machine gun fire and explosions were heard in Kharkiv earlier on Sunday and AFP later saw the wreckage of a Russian armoured vehicle smouldering 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 also claimed it was "entirely" besieging the southern Ukrainian city of Kherson and the city of Berdyansk in the southeast. Both are located close the Crimea peninsula, which Russia annexed from Ukraine in 2014. Ukrainian officials also 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 points and that 4,300 Russian troops had been killed. 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 previous days.
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The city is under a blanket curfew until Monday morning though some residents ventured out regardless. Out for a walk in a park, 41-year-old Flora Stepanova said staying at home watching the news all the time "will drive you crazy". On Saturday, Russia ordered its forces to advance further into Ukraine "from all directions" but soldiers have encountered fierce resistance from Ukrainian troops
Western sources said the intensity of the resistance seems to have surprised Moscow.
Ukraine's army said it held the line against an assault on Kyiv, but was using the curfew to fight Russian "sabotage groups" that had infiltrated the city. On Sunday, Ukraine's general staff urged any foreigners to come to Ukraine "and fight side-by-side with Ukrainians against Russian war criminals". The UN refugee agency (UNHCR) says more than 368,000 people have fled to neighbouring countries, while more than 160,000 are estimated to be displaced within Ukraine.
Pope Francis called for the "urgent" opening of humanitarian corridors for Ukraine to allow even more to leave. AFP saw stationary queues of cars stretching for dozens of kilometres on the roads to Ukraine's border crossings with Poland. "Attacks were everywhere," said Diana, 37, who fled the Ukrainian capital. "My mother is still in Kyiv." Poland, Germany and Austria have said Ukrainians can ride for free on their trains until further notice.
In Romania, which also neighbours Ukraine, Olga, 36, was among hundreds to have crossed the Danube river with her three young children to safety. "My husband came with us as far as the border, before returning to Kyiv to fight," she said. Responding to the invasion, the West said it would remove some Russian banks from the SWIFT bank messaging system, and froze central bank assets -- hitting some of Russia's global trade.
A senior US official said the measures would turn Russia into a "pariah", adding that a task force would hunt down Russian oligarchs' assets. The conflict has rattled particularly former Soviet satellite countries in Eastern Europe who fear their post-Cold War democratic gains could be threatened by Russian aggression. The NATO alliance has said it will, for the first time, deploy part of its rapid response force to the region to reassure eastern allies.
There have also been sanctions and boycotts in the cultural and sporting spheres as well as international travel, with several countries banning Russian airlines from their airspace. In the latest punishment for Putin, a keen judoka, the International Judo Federation said he has been suspended as its honorary president. 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. In an address to parishioners on Sunday, Russia's Orthodox Patriarch Kirill voiced his support, calling Moscow's opponents "evil forces". The rebels have been fighting Ukrainian government forces for eight years in a conflict that has killed more than 14,000 people.
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