Mr Abbott had told reporters he intended to shirtfront the former KGB agent over the downing of Malaysia Airlines flight MH17, though downgraded his pledge to a “robust discussion” on Tuesday.
The withdrawn pledge to shirtfront – an aggressive AFL move where a player uses a front-on bump to knock an opponent down – has since been mocked by Russian media, as well as Russian MP Vyacheslav Nikonov.
The chairman of Russia's education committee told ABC’s Lateline that the comments had been paid little attention by the few people in Russia who had heard them.
“It’s not much news,” he said.
“I don't think there is much attention to what's going on in Australia in Russia, I hate to say that, and probably 99 per cent of the Russians would never hear a name of Australian Prime Minister.”
Mr Nikonov said the “counterproductive” comment would not deter Mr Putin from attending the G20 summit in Brisbane next month, where a formal meeting between the two leaders is yet to be scheduled.
“Putin will be coming to G20 summit, not to see Tony Abbott, and it is for G20 to decide who is coming and for what purpose,” he said.
“Of course Putin will be there, he will be part of the discussion. Russia is the fifth biggest economy and G20 discussing economy more than anything else.”
Russian media invites PM to ‘put up or shut up’
Mr Abbott’s comments have drawn mixed reactions from Australian politicians, with Opposition Leader Bill Shorten saying he didn’t think My Putin would be welcome and Treasurer Joe Hockey Mr Hockey saying the comments were borne from "anger and understandable emotion".
Palmer United Party Senator Jacqui Lambie however has called for both Mr Abbott and Mr Shorten to meet with the Russian leader and “stop acting like hormone affected schoolboys trying to out macho each other on the footie field”.
“Mr Putin is an important and powerful world leader who must be listened to and spoken with,” she said.
Mr Abbott’s comments have made headlines worldwide, including in Russian news outlet Pravda, which described them as “reckless and slanderous”.
Pravda stated that Mr Abbott’s comments were the “most crass example of stupidity the world has seen” in an open letter to the Australian Prime Minister, published overnight.
“If you seriously think you can physically confront your guests and assault a visiting Head of State and walk away freely, then you are mistaken,” it read.
“… While I do not speak for President Putin, if someone "shirt-fronted" me, then I would throw the perpetrator over my shoulder, slam him onto his back on the floor behind me, place my boot on his face and ask "What was that you were saying?" before I saw him scurry away snivelling to his sister's for a clean pair of Y-fronts.”
The open letter, which invited Mr Abbott to “put up or shut up”, followed an earlier column accusing the leader of insolence.