More than 70 Ukrainian soldiers have been killed after Russian troops shelled a military base in the town of Okhtyrka, a city between Kharkiv and Kyiv, according to the regional governor.
Dmytro Zhyvytskyy posted photographs of the charred shell of a four-storey building and rescuers searching rubble.
He said Russian soldiers and local residents were also killed in the attack on Monday, local time.
Russia has been intensifying shelling across the country, bombarding residential districts of Ukraine's second-largest city, Kharkiv, overnight using Grad — or "hail" — rockets.
Meanwhile, a 64-kilometre convoy of Russian tanks and other vehicles threatened the capital Kyiv on the sixth day of the war.
Ukrainian President Volodymyr Zelenskyy said he believed the stepped-up shelling was designed to force him into making concessions during peace talks.
"The talks were taking place against the backdrop of bombing and shelling of our territory, our cities," Mr Zelenskyy said in a video address.
The president gave no details about the hours-long talks themselves, which did not produce any concrete results, but said Ukraine was not prepared to make concessions "when one side is hitting each other with rocket artillery".
Mr Zelenskyy added that Kyiv remained "a key goal" for the Russians and referenced the rocket attacks on Kharkiv, in Ukraine's north-east, which has become a major battleground.
Social media video earlier showed residential areas in Kharkiv being shelled, with apartment buildings shaken by repeated, powerful blasts.
Kharkiv region head Oleg Synegubov confirmed that Kharkiv's administration building had also been hit in an attack, but said the city defences were holding.
Mr Synegubov said Russia launched both Grad rockets and cruise missiles on the city, accusing Moscow of war crimes.
Russia has also been accused of attacking Ukrainians with cluster bombs and vacuum bombs, weapons that have been condemned by a variety of international organisations.
"They wanted to have a blitzkrieg, but it failed, so they act this way," said 83-year-old Valentin Petrovich, using just his first name and his Russian-style middle name because of fear for his safety.
He described watching the shelling from his central city apartment.
Mr Synegubov said Russian artillery had pounded residential districts even though no Ukrainian army positions or strategic infrastructure were there.
At least 11 people were killed, he said.
Kharkiv's mayor Igor Terekhov said four people had died after emerging from a bomb shelter to collect water, as well as a family with three children who had burned to death in a car.
Earlier Interior Ministry adviser Anton Herashchenko said Russian rocket strikes on Kharkiv had killed dozens.
"Kharkiv has just been massively fired upon by Grads," he said in a post on Facebook.
"Dozens of dead and hundreds of wounded."
It was not possible to verify the casualty figures independently.
Video posted by the military showed thick columns of smoke rising from apartment blocks and flashes of flames.
Meanwhile, Moscow's United Nations ambassador, speaking in New York at the start of a UN General Assembly meeting, said the Russian army did not pose a threat to civilians.
More than 500,000 people have fled Ukraine, according to the United Nations refugee agency, setting off a refugee crisis as thousands await passage at European border crossings.
Around 350,000 people have entered Poland, a Polish deputy interior minister said on Tuesday.
Up to 100,000 had crossed the border into Poland in the past 24 hours.
Ukraine's President Volodymyr Zelenskyy urged the West to consider a no-fly zone for Russian aircraft over Ukraine.
"Fair negotiations can occur when one side does not hit the other side with rocket artillery at the very moment of negotiations," Mr Zelenskyy said.
He did not specify how and by whom a no-fly zone would be enforced.
The United States has ruled out sending troops to fight Russia and officials have voiced concern about further escalating tensions between the world's two biggest nuclear powers.
Concerns Russians plan to encircle Kyiv
In Ukraine's capital, Kyiv, explosions were heard before dawn and soldiers set up checkpoints and blocked streets with piles of sandbags and tyres as they waited to take on Russian soldiers.
The 64-kilometre convoy of hundreds of armoured vehicles, tanks, artillery and support vehicles was just 25km from the city centre, according to satellite imagery from the Maxar company.
The company earlier said the convoy was 27km long.
Maxar Technologies also said additional ground forces deployments and ground attack helicopter units were seen in southern Belarus, less than 32km north of the Ukraine border.
The images also captured signs of fighting outside Kyiv, including destroyed vehicles and a damaged bridge.
Messages aimed at the advancing Russian soldiers popped up on billboards, bus stops and electronic traffic signs across the capital.
Some used profanity to encourage Russians to leave. Others appealed to their humanity.
"Russian soldier — Stop! Remember your family. Go home with a clean conscience," one read.
A signboard, normally used for traffic alerts, showed the message: "Putin lost the war. The whole world is with Ukraine."
The United States expects Russian forces to try to encircle Kyiv in the coming days and could become more aggressive out of frustration with their slow advance on the Ukrainian capital, a senior US defence official said.
US officials believe Ukrainian resistance has slowed the progress of Russian troops and planning failures have left some Russian units without fuel or other supplies.
"One of the things that could result is a re-evaluation of their tactics and the potential for them to be more aggressive and more overt, in both the size and scale of their targeting of Kyiv," the official told reporters.
The official, who was speaking on the condition of anonymity and did not provide evidence, said the US had yet to see this happen but was concerned about it.
Russian forces had fired about 380 missiles at Ukrainian targets, the official said, and President Vladimir Putin had committed nearly 75 per cent of his pre-staged combat power into Ukraine.
The official added there were no indications that Belarusian troops were in Ukraine, moving in that direction or preparing to move into Ukraine.
Fighting continues in the south
In other fighting, strategic ports in the country's south came under assault from Russian forces.
Mariupol, on the Sea of Azov, was "hanging on", said presidential adviser Oleksiy Arestovich.
"I sit and pray for these negotiations to end successfully so that they reach an agreement to end the slaughter, and so there is no more war," said Mariupol resident Alexandra Mikhailova, weeping as she clutched her cat in a makeshift shelter.
Around her, parents sought to console children and keep them warm.
Russian forces seized two small cities in south-eastern Ukraine and the area around a nuclear power plant, according to the Interfax news agency, and an oil depot was reportedly bombed in the eastern city of Sumy.
In the resort town of Berdyansk, on the shore of the Azov Sea, residents described the soldiers who captured their town on Sunday as exhausted young conscripts.
"Frightened kids, frightened looks. They want to eat," Konstantin Maloletka, who runs a small shop, said by telephone.
The soldiers went into a supermarket and grabbed canned meat, vodka and cigarettes. "They ate right in the store," he said. "It looked like they haven't been fed in recent days."
Ukrainian protesters there reportedly demonstrated against encroaching Russian troops.
UN human rights chief Michelle Bachelet said at least 102 civilians in Ukraine had been killed since Thursday but the real figure could be "considerably higher".
Ukraine's Health Ministry said on Sunday that 352 civilians, including 14 children, had been killed since the beginning of the invasion.
More than half a million people have fled to neighbouring countries, according to the UN refugee agency.
Assistance from abroad
Partners in the US-led NATO defence alliance were providing Ukraine with air-defence missiles and anti-tank weapons, NATO chief Jens Stoltenberg said.
On Tuesday, Australia said it would provide NATO with around $70 million to purchase missiles and ammunition for Ukraine.
Prime Minister Scott Morrison says the money would go towards purchasing lethal and non-lethal defence equipment.
The Kremlin accused the EU of hostile behaviour, saying weapons supplies to Ukraine were destabilising and proved that Russia was right in its efforts to demilitarise its neighbour.
But there was support for Ukraine from unexpected quarters.
US technology firm Microsoft said it had provided threat intelligence and defensive suggestions to Ukrainian officials about attacks on a range of targets, and also advised the government about attempted cyberthefts of data.
And European football's governing body, UEFA, scrapped sponsorship by the Russian state gas giant Gazprom reported to be worth 40 million euros ($60 million) a season, and UEFA and the global federation FIFA suspended all Russian teams until further notice.
ABC/wires
