The Palmer United Party Senator called for calm in the wake of Mr Abbott’s comments, made one month ahead of the economic leaders' summit in Brisbane.
Senator Lambie said it was essential to keep lines of communication open despite the conflict over the downed Malaysia Airlines flight MH17.
In a statement, she called for both Mr Abbott and Opposition Leader Bill Shorten to “stop acting like hormone affected schoolboys trying to out macho each other on the footie field”.
'Stop acting like hormone affected school-boys trying to out macho each other on the footie field'
“While there are legitimate questions that should be answered over the shooting down of MH17 in July, a tragic event which killed 298 people, including 38 Australian citizens and residents, I don't believe for a minute that Mr Putin would have wanted that disaster and loss of life to happen,” she said.
“Mr Putin is an important and powerful world leader who must be listened to and spoken with.”
Speaking to media in Queensland on Monday, Mr Abbott vowed to “shirtfront” the Russian leader.
“I’m going to be saying to Mr Putin – Australians were murdered and they were murdered by Russian-backed rebels using Russian supplied equipment,” he said.
“We are very unhappy about this. We accept that you didn’t want this to happen, but we now demand that you fully cooperate with the criminal investigation, and if the criminal investigation identifies suspects that you have some influence over, they’ve got to be produced and justice has got to be done.”
Mr Shorten also weighed in on Mr Putin’s attendance at the G20, stating that “I don’t think he’s welcome”.
“I believe that Russia knows more than they've let on about how these missiles were fired,” he said.