Senator Jacqui Lambie said she had handed over the Ulverstone Judo Club's invitation and T-shirt to Russian ambassador in Australia Vladimir Morozov.
The senator said that if a fight was held, the club would stake on Putin, a judo black belt.
According to Lambie, a judo event between Putin and Abbot will be "great for international relations." She said she admires Putin's work as he is serving the interests of Russian people.
On October 13, Abbott vowed to “shirtfront” Putin over the MH17 crash in Ukraine if the Russian president arrives at the G20 Leader's summit in Brisbane scheduled for November 15-16.