LVIV. Ukrainian President Volodymyr Zelenskiy has warned Russian forces they face a fight to the death if they try to occupy the capital Kyiv, as air raid sirens again woke residents on Sunday morning.

"If they decide to carpet bomb 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," Zelenskiy said on Saturday.

The president, who has repeatedly appeared on social media from the capital, said some small towns no longer existed in the third week of Russian attacks, the biggest assault on a European country since World War Two.

Russian shelling has trapped thousands of people in besieged cities and sent 2.5 million Ukrainians fleeing to neighbouring countries.

Ukraine accused Russian forces on Saturday of killing seven civilians in an attack on women and children trying to flee fighting near Kyiv. France said Russian President Vladimir Putin had shown no readiness to make peace.

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 Feb 24. It blames Ukraine for failed attempts to evacuate civilians from encircled cities, an accusation Ukraine and its Western allies strongly reject.

Zelenskiy said 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. Reuters could not verify his statements.

"We still need to hold on. We still have to fight," Zelenskiy said in a video address late on Saturday, his second of the day. Saying about 1,300 Ukrainian troops had been killed, he urged the West to get more involved in peace negotiations.

The United States said it would rush up to $200 million in additional small arms, anti-tank and anti-aircraft weapons to Ukraine, where officials have pleaded for more military aid.

The Kremlin describes its actions as a "special operation" to disarm Ukraine and unseat leaders it calls neo-Nazis. Ukraine and Western allies call this a baseless pretext for a war of choice that has raised fears of wider conflict in Europe.

Zelenskiy discussed the war with German Chancellor Olaf Scholz and French President Emmanuel Macron, who urged Putin to order an immediate ceasefire.

A Kremlin statement on their 75-minute call made no mention of a ceasefire. 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, Ryabkov made no specific threat. Any attack on such convoys before they reached Ukraine would risk widening the war.

Crisis talks between Moscow and Kyiv have been continuing by video link, said Kremlin spokesperson Dmitry Peskov, according to Russia's RIA news agency. He gave no details, but Ukrainian Foreign Minister Dmytro Kuleba said Kyiv would not surrender or accept any ultimatums.

Humanitarian corridors

Russian rocket attacks destroyed a Ukrainian airbase and hit an ammunition depot near Vasylkiv in the Kyiv region, Interfax Ukraine quoted its mayor as saying.

The exhausted-looking governor of Chernihiv, around 150 km (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 has said Russian ground forces were massed 25 km (15 miles) from the centre of Kyiv, while Kharkiv, Chernihiv, Sumy and the key Black Sea port of Mariupol remained encircled under heavy Russian shelling.

The general staff of the Ukraine armed forces said Russia had slowed its offensive and in many places its forces had been stopped. The military's Facebook post did not give details.

Ukrainian officials had planned to use humanitarian corridors from Mariupol in the south as well as towns and villages in the regions of Kyiv, Sumy and some other areas on Saturday.

Around 13,000 people were evacuated from Ukrainian cities on Saturday, said Deputy Prime Minister Iryna Vereshchuk.

The Donetsk region's governor said constant shelling was complicating bringing aid into Mariupol. Fires were burning in the western section of the city and dozens of apartment buildings heavily damaged, according to images taken on Saturday by private US satellite firm Maxar.

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 on Friday. Reuters could not verify casualty figures.

"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.

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 (Doctors without Borders) in Mariupol said.