One reporter on the ground in Kyiv says some people there 'would rather die' than live in Russia.
It comes as Ukraine's president has claimed nearly 9,000 Russian soldiers have been killed since the invasion of his country began a week ago.
Volodymyr Zelenskyy was speaking in a video message in the early hours of Thursday, in which he told the invading forces to "go home".
He warned: "Wherever they go, they will be destroyed.
"They will not have calm here, they will not have food, they will not have one quiet moment.
"The occupiers will receive only one thing from Ukrainians: resistance. Fierce resistance.
"Such resistance that they will forever remember that we don't give up what is ours, that they will remember what a patriotic war is."
It came as Russian troops reached the centre of the Ukrainian port of Kherson, after a day of conflicting claims over whether Moscow had captured its first major urban centre.
Russian troops continue to face stiff resistance from the Ukrainians across the country - both military and civilian - and have yet to overthrow the government in Kyiv.
Bombing in Kharkiv, Ukraine's second-largest city, has also continued - while the Russians have been shelling the city of Izyum, about 75 miles southeast.
Mariupol, a large port city on the Azov Sea, was also encircled by Russian forces, according to Britain's Ministry of Defence.
'A number of loud thuds'
James Waterhouse is the BBC's Kyiv correspondent. He told Newstalk Breakfast there has been more overnight shelling.
"We could hear it from our underground shelter, we heard a number of loud thuds.
"And given that we're two storeys underground, that suggested something either much larger or much closer.
"We've seen footage on social media which showed the whole night sky lit up.
"But we don't know what the targets were, we don't know anything about causalities yet".
James says there were reports that the capital's train station had been hit, which could affect people's ability to leave.
However he says this has since been clarified: "What the authorities tell us this morning is that it was part of a Russian missile that had been taken out by its defence systems, and that there were no casualties.
"But this is not a city relaxing, this isn't a city dropping its guard."
'A tale of two decisions'
He says the determination by people is continuing, noting that some would rather die than live under Russia.
"It's a tale of two decisions, the people above ground are resolute.
"They would fight and they would die - and you believe them when they say it - they would rather die than live in Russia.
"It is a nervous city, people are wondering around with those yellow armbands, they're heavily armed, some are untrained.
"Then we have Russian soldiers as well, they're taking up defensive positions, we don't quite know where.
"They're not thinking about the odds, but we need to be bright-eyed.
"Objectively speaking, Ukrainian forces are outnumbered and they are outmuscled.
"But these images of what's happening to this convoy will of course boost morale to an extent".
'What Kyiv will they find?'
James says the massive convoy outside of the capital has made little progress.
"That 40-mile long Russian convoy on the outskirts is still there but, according to the US, it hasn't moved for the last day and a half.
"Apparently because of a lack of food and fuel for its troops.
"We've seen footage of Russian soldiers looting supermarkets on their way in".
But he says bombardment is also continuing in other cities.
"Kherson is the biggest city yet to fall - it is significant because it is a port city.
"And army chiefs in Ukraine say they are seeing large Russian ships intercept civilian boats, they are seeing Russian ships move towards the southern city of Odessa.
"The south-eastern city of Mariupol is reportedly surrounded by Russian troops.
"Mariupol is one of many cities, key cities, which have had sustained bombardment increasingly on residential areas.
"The worry is that they will fall eventually, given what they're sustaining.
"The mayor said they'd had 14 hours of shelling, hundreds of people have reportedly been killed - but no one can get in there to mount a rescue or recovery operation".
And James adds that no matter what happens, Ukraine will never be the same.
"Then you have the Ukrainians with us who are underground, they've chosen to stay.
"And they are worried; they see what is happening in other locations and they fear the worst.
"And they wonder what Kyiv they will find when they're able to re-emerge at whatever point that is.
"But the future of this country - which has long had to fight for its sovereignty - has changed forever."
Additional reporting: IRN