Ukraine's Defence Ministry has claimed to have killed at least 1,000 Russian troops during the invasion, saying that "Russia has not suffered so many casualties during the fighting in any of its armed conflicts since its inception."

Meanwhile, Russian President Vladimir Putin called on the Ukrainian army to remove leadership in Kyiv.

Russian forces took the air route first to attack the outskirts of Kyiv on Thursday.

On Friday, they entered the northern districts of the Ukrainian capital in a desperate bid to capture Kyiv as the besieged government of Ukraine urged citizens to make Molotov cocktails and defend the city.

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Pedestrians could be seen running for safety as small arms fire and explosions erupted in the Obolonsky district in Kyiv's north.

Larger blasts could be heard in the city centre, where residents spent their first night under curfew and the sounds of bombing, said reports.

Ukraine President Volodymyr Zelensky has vowed to stay in Kyiv as his troops battled Russian invaders.

"(The) enemy has marked me down as the number one target. My family is the number two target. I will stay in the capital. My family is also in Ukraine," Zelensky had said in a video message.

Later he suggested to Russian President Vladimir Putin that they sit down at the negotiation table.

"I would like to address the president of Russia once again ... let us sit down at the negotiation table to stop people dying," Zelenskyy said in a video address that was published on his Telegram channel.

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Earlier, the Ukrainian Defence Force called for civilian recruits regardless of age.

Defence Minister Alexey Reznikov said: "I decided, in agreement with the Commander of the Troops of the Armed Forces of Ukraine ... to involve (those) over 60 years old, who are morally and physically ready to resist and defeat the enemy".

Russian President Vladimir Putin declared war on Ukraine by way of a special military operation on Thursday.

Russian Foreign Minister Sergei Lavrov on Friday said Moscow wants to "free Ukraine from oppression".

"Putin took the decision to conduct a special military operation to demilitarise and de-Nazify Ukraine," Lavrov said at a press conference in Moscow.

Russian forces claimed to have taken control of a vital canal for supply water to Moscow-annexed Crimea, which has been suffering from shortages for the past eight years.

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Russia's invasion of Ukraine has invited severe economic sanctions imposed by US President Joe Biden.

Biden on Thursday announced severe new sanctions on Russia in response to Vladimir Putin authorizing military action against Ukraine, including freezing assets of major banks and cutting off high-tech exports to the country.

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"Export controls will cut off more than half of Russia's high-tech imports. We're prepared to respond to Russia's cyberattack," Biden had said in an address.

He had said the steps imposed in coordination with Europe will block top Russian banks from the US financial system and "cut off more than half of Russia's high-tech imports."