Australia was one of four major offenders, including Canada, Japan and Russia, who are accused of appearing to have withdrawn from attempting to tackle climate change in the Africa Progress Panel's 2015 report.
"With one of the world's highest levels of per capita emissions, Australia has gone from leadership to free-rider status in climate diplomacy," the report said.
It called on the four countries to aim for zero emissions by 2050, with deep reductions by 2030.
But Mr Hunt says Australia should be proud of what it has achieved.
"I can say this, that we are deeply and absolutely engaged," he said at a launch of a tree-planting initiative at Sydney's Bondi Beach.
"There are very few countries that have achieved and beaten their Kyoto 1 targets, there are very few countries that have achieved and will beat their Kyoto 2 targets.
"We will be an ambitious and constructive and engaged player in the post 2020 negotiations."
However, at a United Nations climate change conference in Germany, environment groups believe Australia has embarrassed itself by ducking questions.
The conference is a forerunner to the all-important Paris meeting in December where countries hope to sign a global agreement on climate action.
Several countries questioned the scrapping of the carbon tax and whether the federal government's $2.55 billion direct action policy will be enough to meet Australia's emissions reduction target of five per cent by 2020.
But Mr Hunt said Australia was not grilled at the conference.
"We are asking questions of others and they are rightly asking questions of all countries and so that's how the process should work," he said.
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