Ukraine's government pleaded for help as civilians piled into trains and cars to flee. Thousands of people went deep underground as night fell, jamming Kyiv's subway stations.
Scores of Ukrainians, civilians and service members alike, were killed in the first full day of fighting.
"Russia has embarked on a path of evil, but Ukraine is defending itself and won't give up its freedom," Ukrainian President Volodymyr Zelenskyy tweeted.
Zelenskyy said in a video address that 137 "heroes," including 10 military officers, had been killed and 316 people wounded. The dead included all border guards on the Zmiinyi Island in the Odesa region, which was taken over by Russians.
He concluded an emotional speech by saying that "the fate of the country depends fully on our army, security forces, all of our defenders."
Australia imposes more sanctions
Prime Minister Scott Morrison has unveiled a third tranche of sanctions against Russia, while also providing non-lethal military equipment to Ukraine following the country's invasion.
Mr Morrison said Australia would implement a "rolling wave" of sanctions to put further pressure on Russia.
The new sanctions, which will mirror similar moves from the US and UK, will apply to 300 members of Russia's parliament who voted to authorise the military action, as well as Russian oligarchs of "strategic significance".
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The PM said Australia would work with American authorities to align sanctions against Belarusians who were complicit with Russian acts of aggression.
"Russia has been planning these acts of violence for some considerable period of time, but there must be a cost, there must be a price and it must be imposed by the global community," Mr Morrison told reporters in Adelaide.
"We understand the concern that the threat of sanctions did not lead to (Russia) not going ahead with this. That was not our expectation."
Australia will also work alongside NATO partners to provide non-lethal military equipment and medical supplies to Ukraine.
"We are a long way from Ukraine, and the most effective way is to be doing that with our NATO partners to ensure we can support that commitment," Mr Morrison said.
"We are providing financial support as well as equipment through that NATO channel."
Ukrainians to the head of visa queue
The prime minister also singled out China for failing to call out the Russian invasion of Ukraine and impose sanctions.
On a more immediate note, Ukrainian citizens who have applied for Australian visas have been pushed to the "top of the pile" after the recent Russian invasion.
Scott Morrison said about 430 applications already made for visas by Ukrainians will be prioritised, as global condemnation of Russia's aggression grows.
Mr Morrison said Ukrainians looking to come to Australia in the wake of the military invasion could do so on a number of different visas.
Australian Associated Press
Previous rounds of sanctions have included sanctions on Russian army commanders, mercenaries responsible for attacks and eight members of Russia's security council.
Multiple Russian financial institutions have also been targeted.
