The wild-eyed koala was brought to the Prime Minister by officials at the backstage of the G20 summit.
Modi "tangled" with the koalas deployed by Australia in a a behind-the-scenes diplomatic effort.
Other than the Indian Prime Minister, world leaders including US President Barack Obama, German Chancellor Angela Merkel and Russian President Vladimir Putin also tangled with the koalas backstage, the Herald Sun reported.
Obama was seen to get in on the cuddly action by hugging a koala with Australian Prime Minister Tony Abbott.
After pledging to "shirt-front" the former KGB operative at the international talks, Abbott put the pair's differences briefly aside to introduce Putin to a couple of koalas.
Koala bears are notoriously capricious and sleep for up to 20 hours a day and feed on a diet of special eucalyptus leaves.
They had been training for the high-status visit, acoording to a report in the daily.
Earlier, Australian Prime Minister Tony Abbott's wife Margie Abbott took G20 leaders' partners on a tour of the Lone Pine koala sanctuary in Brisbane where Chinese President Xi Jinping's wife Peng Liyuan and Canadian Prime Minister Stephen Harper's wife Laureen also enjoyed feeding kangaroos and meeting a group of koalas.
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