Abbott -- a conservative who has called the science behind climate change "absolute crap" -- is holding his first talks at the White House a week after Obama unveiled his most ambitious plans yet to reduce carbon emissions blamed for the planet's rising temperatures.
Ahead of his talks, Abbott saluted the historically tight US-Australia alliance, even as he welcomed the rise of China.
"I am confident that the coming century will indeed be the Asian century, but only if America is there too to keep the peace and enforce the rules," Abbott told business leaders at the US Chamber of Commerce.
Obama has sought to "pivot" US foreign policy toward Asia and agreed with the former Labor government to send some 2,500 US Marines to the northern Australian city of Darwin by 2016-2017.
Also Read
While Abbott supports the US military alliance, he has voiced skepticism about climate change, which had been a key priority for former prime minister Kevin Rudd, who was one of Obama's closest international allies.
Abbott has resisted calls by the Obama administration to make climate change a top priority when the Australian leader chairs a summit of the Group of 20 major economies in Brisbane in November.
But he said climate change was just "one of a number of significant issues" and added: "I don't believe that the best way to improve the environment is to clobber the economy."
Abbott earlier met in Canada with Prime Minister Stephen Harper, a fellow conservative who has pushed against stronger international action on climate change.
Abbott met yesterday with US lawmakers including Obama's Republican rivals, who have championed the fossil fuel industry.
Obama has pledged to reduce carbon emissions from power plants by 30 per cent by 2030 from 2005 levels. The European Union has historically taken the lead on tackling climate change.