Mr Albanese says the two nations will continue to celebrate "the bonds of humanity through which we will surely find the peace we seek".
"On your Independence Day, Australia celebrates the contribution of Australians of Ukrainian descent and the more than 3800 Ukrainians we have welcomed since February," he said in a statement on Wednesday.
"You share gifts of culture, faith and history that enrich us all.
"We are one with you and we share in your sorrow at the tragedy unfolding in Ukraine."
Australia was steadfast in its support for the besieged nation as it struggles to defend itself against Russian aggression, he said.
"Ukraine's resistance against Russia's brutal invasion is a test of the world's commitment to the ideals of democracy and the integrity of international borders," Mr Albanese added.
The opposition also expressed support on Wednesday, calling on the federal government to do everything necessary to ensure Australia remains at the forefront of support for Ukraine.
"Australia has stood shoulder-to-shoulder with Ukraine and continues to condemn Russia's abhorrent actions," Opposition Leader Peter Dutton said in a joint statement with his defence and foreign affairs spokesmen.
"This 31st Independence Day will be a difficult day for many Ukrainians, as it also marks exactly six months since the beginning of Russia's invasion of Ukraine.
"We grieve for those whose lives have been lost, including many women and children."
Public celebrations in Ukraine have been cancelled and the US warned its citizens to leave amid fears of new Russian attacks.
President Volodymyr Zelenskiy warned of more strikes as officials banned public gatherings in the capital Kyiv and imposed a curfew in the eastern city of Kharkiv.
Mr Zelenskiy also promised "a powerful response" against Russia at a news conference on Tuesday as his government displayed burnt-out Russian tanks in central Kyiv in an act of defiance.
Ukraine broke free of the then-Soviet Union in August 1991 after an overwhelming majority of Ukrainians voted in a referendum to declare independence.
with Reuters
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