Ukraine dismissed Moscow's offer to set up humanitarian corridors from several bombarded cities on Monday after it emerged some routes would lead refugees into Russia or Belarus.
The Russian proposal of safe passage from Kharkiv, Kyiv, Mariupol and Sumy had come after terrified Ukrainian civilians came under fire in previous ceasefire attempts.
Russia unleashed another night of relentless attacks from air, land and sea, compounding the humanitarian disaster that has pushed more than 1.5 million people across Ukraine's borders.
International sanctions intended to punish Moscow have so far done little to slow the invasion, and Washington said it was now discussing a ban on Russian oil imports with Europe.
Oil prices soared to near a 14-year high and gas prices rocketed on the developments while stock markets plunged as investors worried about the fallout on the global economy.
Horrifying scenes at the weekend saw Ukrainian civilians being cut down as they tried to flee various cities, adding to the international outrage.
Moscow's defence ministry had earlier Monday announced new plans for humanitarian corridors, with the defence ministry confirming a "regime of silence" had started at 0700 GMT (1230 IST).
But several routes led into Russia or its ally Belarus, raising questions over the safety of those who might use them.
"This is not an acceptable option," Ukrainian Deputy Prime Minister Iryna Vereshchuk said. The civilians "aren't going to go to Belarus and then take a plane to Russia".
Moscow had said the decision was taken after a "personal request" by French President Emmanuel Macron, who spoke with Russia's Vladimir Putin on Sunday.
Macron's office however denied there had been such a request.
AFP journalists saw thousands of civilians early Monday fleeing the fighting via an unofficial humanitarian corridor in Irpin, a strategic suburb west of Kyiv.
"I am so happy to have managed to get out," said Olga, a 48-year-old woman leaving with her two dogs.
Children and the elderly were carried on carpets used as stretchers on the route, which leads over a makeshift bridge and then a single path secured by the army and volunteers.
Desperate people abandoned pushchairs and heavy suitcases to make sure they could get on the buses out of the war zone.
A day earlier a family of two adults and two children were killed by a shell as they tried to leave the war-torn area in scenes that horrified the world.
"They are monsters. Irpin is at war, Irpin has not surrendered," mayor Oleksandr Markushyn said on Telegram, adding that he had seen the family killed with his own eyes.
Two recent attempts to allow some 200,000 civilians to leave the key Azov Sea port of Mariupol, where the International Committee of the Red Cross warned of "devastating scenes of human suffering", have also ended in disaster.
One family which did manage to leave the city described spending a week without heat or electricity and running out of food and water.
"On the road, we saw there were bodies everywhere, Russians and Ukrainians... we saw that people had been buried in their basements."
There was no let-up in the violence overnight into Monday, with air sirens sounding in cities across the country, and intense aerial bombardment in Ukraine's second city Kharkiv, which has endured almost non-stop fire in recent days.
"The enemy continues the offensive operation against Ukraine, focusing on the encirclement of Kyiv, Kharkiv, Chernihiv, Sumy and Mykolayiv," the General Staff of the Armed Forces of Ukraine said in a statement.
The mayor of Gostomel, the town north of Kyiv that is home to a crucial military airfield, was shot dead by Russian forces along with two other people while "distributing bread to the hungry and medicine to the sick," local officials said.
The bodies of nine people -- five civilians and four soldiers -- were found in the rubble of Vinnytsia airport in central Ukraine after it was destroyed in a Russian missile attack on Sunday, rescue services said.
However a key town in the Kharkiv region, Chuguiv, has been retaken in a counterattack by Ukrainian forces, Anton Gerashchenko, an aide to the interior minister, wrote on Telegram.
Ukraine's President Volodymr Zelenskyyy renewed calls for the West to boycott Russian exports, particularly oil, and to impose a no-fly zone to stop the carnage.
"How many more deaths and losses must it take to secure the skies over Ukraine?" he said in a video message.
Twelve days of fighting have killed hundreds of civilians and wounded thousands. An unending stream of people -- mostly women and children -- has poured into neighbouring countries in what the UN calls Europe's fastest-growing refugee crisis since World War II.
Western allies have imposed unprecedented sanctions against businesses, banks and billionaires in a bid to choke the Russian economy and pressure Moscow to halt its assault.
But Russian President Vladimir Putin has equated global sanctions with a declaration of war and warned that Kyiv is "putting in question the future of Ukrainian statehood" by continuing to resist.
Moscow has been forced to restrict sales of essential goods to limit black-market speculation, while on Sunday payment giant American Express halted operations there, a day after Visa and MasterCard announced similar steps.
Streaming giant Netflix suspended its service in Russia while social media titan TikTok halted the posting of new videos from Russia.
Despite harsh punishments for those voicing dissent, protests in Russia against the Ukraine invasion have continued, with more than 10,000 people arrested since it began.
Putin has pledged the "neutralisation" of Ukraine "either through negotiation or through war", and expectations remain low for a third round of Russian-Ukrainian talks set for Monday.
China said on Monday it was open to helping mediate peace, but stressed that the friendship between close allies Beijing and Moscow remained "rock solid".
The International Court of Justice meanwhile began hearing Ukraine's appeal for it to order Russia to halt the fighting, but Moscow declined to attend the sitting of the UN's top court in The Hague.
NATO allies have so far rebuffed Ukraine's calls for a no-fly zone, with one senior US senator, Marco Rubio, saying Sunday that it could lead to "World War III" against nuclear-armed Russia.
Putin has threatened "colossal and catastrophic consequences not only for Europe but also the whole world" if a no-fly zone is imposed.
Kyiv also has urged the West to boost its military assistance, with Zelenskyy pleading for Russian-made planes that his pilots are trained to fly.
US Secretary of State Antony Blinken said Washington was "working actively" on a deal with Poland to supply it with American jets.
Moscow has also warned Ukraine's neighbours against hosting Kyiv's military aircraft, saying they could end up involved in armed conflict.
Weapons, ammunition and funds have poured into Ukraine from Western allies as they seek to bolster Kyiv.
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