Russian and Ukrainian delegates have spent five hours discussing a ceasefire – all the while attacks on the ground showed Russian President Vladimir Putin is in no mood for peace.
Ukraine has accused Russia of committing war crimes by firing rockets at civilian housing in the country’s second-largest city, Kharkiv.
Russian forces also seized two small cities in south-eastern Ukraine and the area around a nuclear power plant, the Interfax news agency reported.
A senior US defence official said Russia had fired more than 350 missiles at Ukrainian targets since Thursday, some hitting civilian infrastructure.
The Kremlin has maintained it is only targeting state infrastructure.
That has done little to quell the fears of the innocent men, women and children sheltering in basements and train stations.
At least 102 civilians in Ukraine have been killed since Thursday, with a further 304 wounded, but the real figure is feared to be “considerably higher”, UN human rights chief Michelle Bachelet said on Monday.
More than half a million people have fled to neighbouring countries, according to the UN Refugee Agency.
Shelling continued – and Russian military were massed 30 kilometres north of the capital Kyiv, according to British intelligence – even while delegates from both sides met in Belarus where they had been promised a safe space for negotiations.
After five hours, Russia and Ukraine could not reach an agreement.
Talks had started with the aim of an immediate ceasefire and the withdrawal of Russian forces, the Ukrainian president’s office said.
Russia was cagier about the details, with the Kremlin declining to comment on the country’s aim.
An aide to Russian President Vladimir Putin, Vladimir Medinsky, said on Tuesday morning the two sides “found certain points on which common positions could be foreseen”.
Mykhailo Podolyak, a top adviser to Ukrainian President Volodymyr Zelensky, said the meeting had been difficult.
“The Russian side, unfortunately, still has a very biased view of the destructive processes it has launched,” he said in a tweet.
“The next meeting will take place in the coming days on the Polish-Belarusian border, there is an agreement to that effect.”
The Ukrainian president, meanwhile, has issued a warning to invaders as he announced 4500 Russians had been killed.
“Abandon your military equipment and leave,” Mr Zelensky said.
“Do not trust your commanders, do not trust their propaganda…just save your lives…leave.”
Mr Zelensky also signed an application for membership of the European Union.
“We appeal to the European Union for Ukraine’s immediate accession under a new special procedure,” Mr Zelensky said in the video broadcast from Kyiv and shared on his official social media pages.
“Our goal is to stand alongside all Europeans and, most importantly, to stand on their level…I am sure we deserve it.”
Partners in the US-led NATO defence alliance were providing Ukraine with air-defence missiles and anti-tank weapons, Chief Jens Stoltenberg said in a tweet.
The Kremlin accused the European Union of hostile behaviour, saying weapons supplies to Ukraine were destabilising and proved that Russia was right in its efforts to demilitarise its neighbour.
The UN Human Rights Council agreed on Monday to Ukraine’s request to hold an urgent debate this week on Russia’s invasion, minutes after Kyiv’s envoy told the Geneva forum that some of Moscow’s military actions “may amount to war crimes”.