Fighting against Russian forces is continuing across Ukraine but the capital and other strategically important cities remain under the control of the Ukrainian army, President Volodymyr Zelenskiy says.
The Kremlin was pressing ahead for a third day on a mission to capture the centre of Kyiv and "install their puppets here," Zelenskiy said in a Saturday afternoon video update.
But fears of urban warfare in the capital have not yet come to pass even though the city was rocked by the sounds of gunfire and explosions overnight.
Zelenskiy had earlier warned Ukrainians that Russian troops would likely "storm" the city during the night and called on people to "stop the enemy wherever possible".
As the sun rose over Kyiv, Zelenskiy took to social media to reject reports suggesting he had fled the country and declared while strolling down a city street: "I'm still here."
After the night of ground and air attacks in the Kyiv area and elsewhere, he said Ukrainians would not lay down their weapons or surrender, as Russian President Vladimir Putin demanded.
Mykhailo Podolyak, an advisor to Zelenskiy, said Russian forces were still trying to move a large number of troops and equipment into the city and that fighting was taking place in outlying areas.
But Ukrainian troops were mounting a strong defence and "both in the city itself and on the outskirts of Kyiv, the situation is under control," Podolyak said in comments carried by Ukraine's UNIAN news agency.
Authorities told people in Kyiv to hunker down in bomb shelters if they can and take precautions like staying away from windows.
"Last night was difficult but there are no Russian troops in the city," Mayor Vitali Klitschko said in a video published on the Telegram news channel on Saturday morning.
But he added: "The enemy is trying to advance into the city."
Kyiv's infrastructure was still intact and underground trains were running.
The Ukrainian army meanwhile called on the population to help stop the invasion in every possible way.
"Cut down trees, build barricades, burn tyres! Use everything available!" the armed forces said in a statement quoted by the country's UNIAN news agency.
Earlier, Ukraine's foreign minister posted an image of smoke coming out of a Kyiv high-rise that had at least four floors destroyed during fighting.
It was not yet clear if there were casualties.
The Ukrainian army said it repelled an attack on a barracks in Kyiv's west, only about 7km from the city centre.
Photos showed the site on fire while the sound of gunfire was audible on videos shared on social media.
Earlier in the night, there were reports that Russian troops tried to attack a combined heat and power plant in the far northeast of the city.
Both Russia and Ukraine released new figures on the war's toll in terms of lives and infrastructure, although the information could not be independently verified.
Russia has crippled the operations of more than 800 Ukrainian military infrastructure sites, including airfields, command posts, anti-aircraft missile systems and radar stations, the Defence Ministry in Moscow said on Saturday, the third day of Russia's offensive.
Russia insists it is only going after military targets - despite allegations to the contrary from Kyiv and witnesses on the ground - and says it is Ukrainian forces that are shelling residential areas in the eastern Donbass region.
Ukraine's Defence Ministry said 3500 Russian soldiers had been killed and 200 others captured.
In addition, it said 14 planes, eight helicopters and 102 tanks as well as more than 530 other military vehicles were destroyed.
According to the Ukrainian government, at least 198 civilians have been killed and 1115 people injured across the country, including 33 children, after three days of attacks by Russian ground and air forces.
Among the dead were three children, Health Minister Viktor Liashko wrote on Facebook.
Meanwhile, Ukrainians continued to try and escape the violence by crossing into neighbouring countries.
The Polish deputy interior minister said on Saturday about 100,000 Ukrainian refugees have arrived in the country since the beginning of the Russian invasion.