Ihor Tkachenko, a computer engineer from Kyiv, is not able to sign up to the civil defence forces that have sprung up across Ukraine to help resist the Russian invasion.

With a severe limp he is unable to meet the physical requirements, but that has not stopped him staying in the capital along with many others. Tens of thousands of people have also fled to the relative safety of the west.

"My wife and daughter are safe and in a village in the Carpathians and I wanted to remain," the 43-year-old told Reuters on Wednesday, referring to the mountain range in the far west of the country.

"If they (the Russians) enter the city I can always throw a Molotov cocktail from my balcony," he added, standing amid debris strewn across the ground close to Kyiv's main TV tower which was struck in a deadly Russian attack the day before.

"I have a dog. It is a fearless beast, and we will die together."

Wearing a blue tracksuit, Tkachenko surveyed the wreckage around him. Near the tower a gym was gutted by the force of the blast and exercise equipment still smouldered.

"This was not a military target, this was made to intimidate us," he added, carefully negotiating broken bricks and shards of timber and metal.

Led by President Volodymyr Zelenskiy, who has appealed to his people to repel invading forces and who remains in Kyiv to rally support, thousands of Ukrainians have vowed to take up arms and do what they can to protect their country.

Russian forces have bombarded cities including Kyiv and Kharkiv and have fought to seize urban centres, but local resistance has been strong and some military experts say Moscow has been taken by surprise.

Russian President Vladimir Putin says his troops have launched a "special military operation" in neighbouring Ukraine to remove a security threat.

Outside one of the huge apartment blocks built on the banks of the Dnipro river in Kyiv, Inna, a housewife, looked exhausted as she went to her local supermarket to stock up on food.

She said she had barely slept, interrupted by artillery fire northwest of the city.

"I am tired from constant crying, worrying and ... thinking what the hell are they doing in our country," she said.

"Honestly, I am on the verge of taking up a gun and going to the frontline. I will do whatever is needed to help."

(Writing by Mike Collett-White; Editing by Alexandra Hudson)