Russia was axed from the G7 meeting in Brussels over its annexation of Crimea, with Putin cold-shouldered by the United States and its allies since the March seizure of the peninsula.
Australia is the current holder of the rotating G20 presidency and hosts the leaders' summit in Brisbane in November.
Abbott said that while he shared serious concerns over Russia's role in Ukraine, there was no indication Putin would not be invited.
"Obviously there are very grave concerns about the behaviour of Russia in Ukraine and I can understand why the G7 leaders were reluctant to sit down with President Putin at this time.
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"But when it comes to the prosperity of the world, when it comes to the management of international finances, when it comes to harmonisation of taxation rules, when it comes to trying to promote global growth, I think it is best if we can include Russia.
The G7 groups Britain, France, Germany, Italy, Japan, Canada and the United States with US President Barack Obama on Thursday saying Russia had to recognise Ukraine's president-elect Petro Poroshenko.
He also said Moscow must withdraw troops from Ukrainian borders and stop backing the pro-Moscow rebels destabilising eastern Ukraine.
In a statement after their summit, the leaders of the Group of Seven industrialised nations warned of tougher sanctions if the conditions set out by Obama were not met.