The Ukrainian Foreign Ministry has called Russia barbaric for launching a missile strike on a TV tower next to a memorial commemorating the victims of one of the biggest single massacres of Jews by Nazi Germany.
Emergency services in Ukraine said five people were killed in the strike on the tower in Kyiv and that many more were injured.
"Russian troops fired on the TV tower, near the Memorial complex #BabynYar," Ukraine's Foreign Ministry said.
Foreign Minister Dmytro Kuleba called the attack "evil" and condemned Russia for its actions.
Ukrainian President Volodymyr Zelenskyy said history was repeating as he shared news of the attack at the site commemorating the victims of Babyn Yar, where over 30,000 Jews were killed over two days in September, 1941.
The strike on the TV tower came as the United States said Russia's advance on Kyiv had stalled.
A senior US defence official said Russian forces were facing logistical challenges, with some units running out of food.
Earlier, a 64-kilometre convoy of Russian tanks and other vehicles had been seen just 25km from the city centre, according to satellite imagery from the Maxar company.
Mariupol under relentless shelling
There was constant shelling in Ukraine's Mariupol port, and civilian targets in the country's second-largest city Kharkiv continued to be hit, as Russia started day six of its invasion.
The mayor of Mariupol said five days of strikes had killed civilians and damaged infrastructure.
A Russian-backed separatist leader in eastern Ukraine said his forces were aiming to "directly encircle" the city of 150,000 in south-eastern Ukraine.
Residential areas are being increasingly targeted across the country, with an advisor to Ukraine's president accusing Russia of deliberately shelling cities to spread panic among Ukrainians.
Zelenskyy calls Kharkiv attacks acts of 'terror'
In Kharkiv, an eastern city with a population of about 1.5 million, videos posted online showed explosions hitting the region's Soviet-era administrative building.
Images posted online showed the building's facade and interior badly damaged by a powerful explosion that also blew up part of its roof.
The state emergencies agency said the attack wounded six people, including a child.
Regional administration chief Oleh Sinehubov said that least 11 people were killed and scores of others were wounded in overnight shelling of the city.
Mr Zelenskyy said the Russian artillery attacks on Kharkiv amounted to state terrorism and called on the international community to recognise it as such.
"The terror aims to break us, to break our resistance," he said in a video address shared on social media, describing Kyiv and Kharkiv as Russia's main targets.
More than 70 Ukrainian soldiers were killed after Russian troops shelled a military base in the town of Okhtyrka, between Kharkiv and Kyiv, according to the regional governor.
Nearly a week since Moscow unleashed its war on its neighbour, its troops have failed to capture a single major Ukrainian city after running into fierce resistance.
But it still has more forces to throw into the fight even though Russian President Vladimir Putin faces worldwide condemnation and international sanctions for his actions.
Diplomats boycott Russian foreign minister at UN
Dozens of diplomats from the European Union (EU), United States and Britain walked out of a speech by Russian Foreign Minister Sergei Lavrov to the top UN human rights forum on Tuesday, according to a Reuters witness.
Mr Lavrov was addressing the UN Human Rights Council remotely, having cancelled his attendance earlier due to what the Russian mission in Geneva said on Monday were EU states blocking his flight path.
Oil company Shell became the latest Western firm to announce it was pulling out of Russia.
The sanctions and global financial isolation have already had a devastating impact on Russia's economy, with the rouble in freefall and queues outside banks as Russians rush to salvage their savings.
Former ABC Russia correspondent Michael Brissenden said the Ukrainian resistance was settling in for the long haul.
He said the Ukrainians were "out-classed and out-numbered" but even if the Russian forces took the capital, the resistance would not stop.
"We are seeing a lot of interest from veterans all over the world who are interested in going to help with the fight, but a lot of expatriates will be interested to sign up to this sort of 'foreign legion' idea which has been floated by [Ukraine President] Zelenskyy."
Russia accused of using banned cluster munitions
Human rights groups and Ukraine's ambassador to the United States accused Russia of using cluster bombs and vacuum bombs, weapons that have been condemned by many organisations.
Kremlin spokesman Dmitry Peskov rejected the accusations and insisted on Tuesday that "the Russian troops don't conduct any strikes against civilian infrastructure and residential areas".
The UN human rights office said it had recorded the deaths of 136 civilians, including 13 children, in Ukraine since the start of Russia's invasion, but warned the toll may be far higher.
It has also recorded 400 civilians injured in the conflict, among them 26 children.
"Most of these casualties were caused by the use of explosive weapons with a wide impact area, including shelling from heavy artillery and multiple-launch rocket systems, and air strikes," it said.
Ukraine's general staff said Russian losses included 5,710 personnel, 29 destroyed and damaged aircraft and 198 tanks, all figures that could not be verified.
Russia has not given a full account of its battlefield losses, but pictures from Ukraine have shown burnt-out Russian tanks and bodies on the road where they have been attacked by Ukrainian defenders.
Talks held on Monday at the Belarus border failed to reach a breakthrough.
Negotiators have not said when a new round will take place.
Public health experts have warned that Ukraine is already running low on critical medical supplies and fears of a wider public health crisis are growing as people flee their homes and health services and supplies are interrupted.
More than 500,000 people have fled Ukraine, according to the UN refugee agency, setting off a refugee crisis as thousands await passage at European border crossings.
At the United Nations, the General Assembly met ahead of a vote to isolate Russia, deploring Moscow's "aggression against Ukraine" and demanding its troops stop fighting and withdraw.
UN Secretary-General Antonio Guterres described Mr Putin's decision on Sunday to put Russia's nuclear deterrent on high alert as a "chilling development", telling the General Assembly that nuclear conflict was "inconceivable".
Wires/ABC
