Ukraine has accused Russian forces of killing seven civilians in an attack on women and children trying to flee fighting near Kyiv, and France said Russian President Vladimir Putin had shown he was not ready to make peace.
With Russia's invasion in its third week, the Ukrainian intelligence service said the seven, including one child, were killed as they fled the village of Peremoha and that "the occupiers forced the remnants of the column to turn back".
Reuters was unable immediately to verify the report and Russia offered no immediate comment.
Moscow denies targeting civilians since invading Ukraine on 24 February. It blames Ukraine for failed attempts to evacuate civilians from encircled cities, an accusation Ukraine and its Western allies strongly reject.
Around 13,000 people were evacuated from a number of Ukrainian cities today, said Deputy Prime Minister Iryna Vereshchuk, almost twice the number who managed to get out the previous day.
Ms Vereshchuk said in an online message that no one had managed to leave the besieged city of Mariupol and blamed obstruction by Russian forces. Moscow had accused Ukrainian forces of intentionally trapping people there.
Ukrainian President Volodymyr Zelensky said earlier that Moscow was sending in new troops after Ukrainian forces put 31 of Russia's battalion tactical groups out of action in what he called Russia's largest army losses in decades. It was not possible to verify his statements.
He also said about 1,300 Ukrainian troops had been killed so far and urged the West to get more involved in peace negotiations. The president suggested Russian forces would face a fight to the death if they sought to enter the capital.
"If they decide to carpet bomb (Kyiv), and simply erase the history of this region ... and destroy all of us, then they will enter Kyiv. If that's their goal, let them come in, but they will have to live on this land by themselves," he said.
Mr Zelensky discussed the war with German Chancellor Olaf Scholz and French President Emmanuel Macron, and the two leaders then spoke to Mr Putin by phone and urged him to order an immediate ceasefire.
A Kremlin statement on the 75-minute call made no mention of a ceasefire and a French presidency official said: "We did not detect a willingness on Putin's part to end the war."
Russian Deputy Foreign Minister Sergei Ryabkov accused the United States of escalating tensions and said the situation had been complicated by convoys of Western arms shipments to Ukraine that Russian forces considered "legitimate targets".
In comments reported by the Tass news agency, Mr Ryabkov made no specific threat, but any attack on such convoys before they reached Ukraine would risk widening the war.
Responding to Mr Zelensky's call for the West to be more involved in peace negotiations, a US State Department spokesperson said: "If there are diplomatic steps that we can take that the Ukrainian government believes would be helpful, we're prepared to take them."
Crisis talks between Moscow and Kyiv have been continuing via a video link, Kremlin spokesperson Dmitry Peskov was quoted as saying by Russia's RIA news agency. He gave no details but Ukrainian Foreign Minister Dmytro Kuleba said Kyiv would not surrender or accept any ultimatums.
Air raid sirens blared across most Ukrainian cities today, local media reported.
Russian rocket attacks destroyed a Ukrainian airbase and hit an ammunition depot near the town of Vasylkiv in the Kyiv region, Interfax Ukraine quoted its mayor as saying.
The exhausted-looking governor of Chernihiv, around 150km (100 miles) northeast of Kyiv, gave a video update in front of the ruins of the city's Ukraine Hotel.
"There is no such hotel any more," Viacheslav Chaus said, wiping tears from his eyes. "But Ukraine itself still exists, and it will prevail."
Britain's defence ministry said fighting northwest of the capital continued, with the bulk of Russian ground forces 25km (16 miles) from the centre of Kyiv, which it has said Russia could attack within days.
Kharkiv, Chernihiv, Sumy and Mariupol remained encircled under heavy Russian shelling, it said.
Russia's invasion has been almost universally condemned around the world and has drawn tough Western sanctions.
The Russian bombardment has trapped thousands of people in besieged cities and sent 2.5 million Ukrainians fleeing to neighbouring countries. Mr Zelensky said the conflict meant some small Ukrainian towns no longer existed.
The United States said it would rush up to $200m in additional small arms, anti-tank and anti-aircraft weapons to Ukraine, where officials have pleaded for more military aid.
Russia calls its actions in Ukraine a "special operation" that it says is not designed to occupy territory but to destroy its neighbour's military capabilities and "de-Nazify" the country.
Ukrainian officials had planned to use humanitarian corridors from Mariupol as well as towns and villages in the regions of Kyiv, Sumy and some other areas today. But Russian shelling threatened attempts to evacuate trapped civilians, they said.
A senior Russian defence ministry official said the humanitarian situation in Ukraine continued to decline rapidly and blamed Ukrainian fighters, accusing them of mining neighbourhoods and destroying bridges and roads, the RIA news agency reported.
Russian officials have previously accused Ukrainian forces of shelling their own people and then seeking to blame Moscow, allegations that Kyiv and Western nations dismissed as lies.
The governor of the Kyiv region, Oleksiy Kuleba, said fighting and threats of Russian air attacks were continuing today though some evacuations were proceeding.
The Donetsk region's governor said constant shelling was complicating bringing aid into the southern city of Mariupol.
Images taken today by private US satellite firm Maxar showed fires burning in the western section of Mariupol and dozens of apartment buildings heavily damaged.
"There are reports of looting and violent confrontations among civilians over what little basic supplies remain in the city," the UN's Office for the Coordination of Humanitarian Affairs said.
"Medicines for life-threatening illnesses are quickly running out, hospitals are only partially functioning, and the food and water are in short supply."
People were boiling ground water for drinking, using wood to cook food and burying their dead near where they lay, a staff member for Medecins Sans Frontieres in Mariupol said. "Neighbours just dig a hole in the ground and put the dead bodies inside," he said.
At least 1,582 civilians in Mariupol have been killed as a result of Russian shelling and a 12-day blockade, the city council said yesterday. It was not possible to verify casualty figures.
Efforts to isolate Russia economically have stepped up, with the United States imposing new sanctions on senior Kremlin officials and Russian oligarchs yesterday.
European Commission President Ursula von der Leyen said today that the EU would suspend Moscow's privileged trade and economic treatment, crack down on its use of crypto-assets, and ban the import of iron and steel goods from Russia, as well as the export of luxury goods in the other direction.