It follows similar moves by the United States and the United Kingdom at the start of April.

Mr Putin's daughters Maria Vladimirovna Vorontsova, 37, and Katerina Vladimirovna Tikhonova, 36, are described by the US as a tech executive who supports the Russian government and defence industry, and the leader of state-funded programs receiving billions of dollars from the Kremlin.

The US believes some of Mr Putin's assets have been hidden by family members.

Mr Lavrov's daughter, Ekaterina Sergeevna Vinokurova, holds Russian and US citizenship.

The 144 senators targeted provided support to Mr Putin's illegitimate recognition of the independence of the Ukrainian regions of Donetsk and Luhansk.

Mr Putin used that declaration to justify the invasion of Ukraine two days later.

The new sanctions bring the list that Australia has targeted to nearly 750 individuals and entities in response to Russia's invasion of Ukraine.

Foreign Minister Marise Payne said Australia will continue to increase the costs on Russia and those "who bear responsibility for Russia's unjustified and unprovoked aggression in Ukraine or hold levers of influence".

"The Australian government again reiterates our strongest support for Ukraine's sovereignty and territorial integrity, and for the people of Ukraine," Senator Payne said.

"We again call upon Russia to withdraw its military forces immediately from Ukraine."

Australian Associated Press