US President Joe Biden branded Vladimir Putin a "war criminal" Wednesday as the Russian leader's onslaught in Ukraine claimed more civilian lives, and a theatre where "hundreds" were sheltering was destroyed by bombing.

Biden's rebuke -- his sharpest yet -- came after Ukraine's leader Volodymyr Zelensky made a searing appeal for help to the US Congress and the president himself, who responded by pledging $1 billion in new weapons to fight Russia's invading army.

Officials in the port city of Mariupol were struggling to count the dead at the Drama Theatre, where thick smoke rose from the rubble of the building that had the word "children" painted in large Russian letters on the ground outside.

It was the latest in a litany of assaults on civilians across Ukraine since Putin invaded on February 24 that has included homes, hospitals, ambulances and food queues.

"I think he is a war criminal," Biden told reporters of his Russian counterpart, the first time he has used the phrase.

Biden's spokesperson added that he had spoken "from his heart" -- but the Kremlin quickly punched back, calling the comment "unacceptable and unforgivable on the part of the head of a state, whose bombs have killed hundreds of thousands of people around the world."

So far the destruction that has marked other cities has been halted outside Kyiv.

But dull booms echoed across the capital's deserted streets Wednesday, with only an occasional vehicle passing through sandbagged checkpoints, and very few permits granted to break its latest curfew.

Kyiv has been emptied of around half of its 3.5 million people.

"It's worrying, of course. It's war after all. But we try to stay calm, we won't allow panic," said Eduard Demenchuk, a private-security employee in his 50s, was among those who have stayed.

"If need be, we will take arms and will stand to defend the city," he told AFP by telephone, after stocking up on groceries.

The attack on the theatre in Mariupol is the latest atrocity in the southern city, which has been besieged for weeks, with more than 2,000 people killed so far.

Mariupol city authorities said Russia "purposefully destroyed" the theatre, though Moscow blamed Ukrainian forces for the blast.

Efforts to establish the number of casualties were hampered by nearby shelling.

President Zelensky gave no further details in his regular evening address, saying only "my heart is breaking seeing what Russia is doing to our people, to our Mariupol."

Also on Wednesday at least 15 civilians were killed in the northern city of Chernihiv.

Ten of them died while queueing to collect bread. Another five, including three children, were killed when Russian forces shelled a residential building.

As the civilian toll climbed, the World Health Organization warned that Ukraine's health system was "teetering on the brink."

"This is about the destruction of hope ... This is the most basic of human rights and it has been directly denied," WHO official Michael Ryan said in Geneva.

The conflict has already sent more than three million Ukrainians fleeing across the border, many of them women and children.

Ukraine authorities said 103 children have been killed since the invasion began.

In a virtual address to Congress, Zelensky invoked Pearl Harbor, the 9/11 attacks and Martin Luther King Jr as he showed lawmakers a video of the wrenching effect of three weeks of Russian attacks.

Zelensky, dressed in military green, demanded Washington and its NATO allies impose a no-fly zone, so that "Russia would not be able to terrorize our free cities."

Switching to English, Zelensky addressed Biden directly, saying: "I wish you to be the leader of the world. Being the leader of the world means to be the leader of peace."

Biden and NATO have resisted Zelensky's pleas for direct involvement against nuclear-armed Russia, warning it could lead to World War Three -- though Zelensky told NBC that "may have already started."

On Wednesday Biden announced the United States' latest package of new weapons aid to Ukraine added up to $1 billion and that the US would help Ukraine acquire longer-range anti-aircraft weapons.

Putin at a televised government meeting insisted the invasion was "developing successfully," adding "we will not allow Ukraine to serve as a springboard for aggressive actions against Russia."

Western sanctions against Putin's regime have pushed Russia close to a default on its foreign debts.

Moscow was due Wednesday to pay $117 million on two dollar-denominated bonds -- the first interest payment since it was largely shut out of the Western financial system.

The Kremlin has sought to suppress domestic opposition to the war, blocking access to Russian and foreign-based media including the BBC and investigation website Bellingcat.

In his speech Putin claimed Western leaders gave him "no option to resolve the process in a peaceful way", and Kyiv and Moscow remained far apart at another round of sputtering talks Wednesday.

Kremlin spokesman Dmitry Peskov said a "compromise" outcome would center on Ukraine becoming a neutral state comparable to Sweden and Austria. But Zelensky's office gave the idea short shrift.

There was one glimmer of hope that talks might yet bear fruit, as the United States and Russia made their first high-level contact since the invasion began.

And many Ukrainians themselves remained defiant.

"Used to be rackets and strings, now this," the 33-year-old wrote on Instagram alongside a photo of a rifle, helmet and flak jacket.

The mayor of Ukraine's southern city of Melitopol was released days after Kyiv said he was abducted by Russian forces.

"Thank you for not abandoning me," Ivan Fedorov told Zelensky, according to video of their phone call posted on Telegram.

"I will need one or two days to recover and then I will be at your disposal to contribute to our victory."