Trump's decision, which has been roundly denounced by the international community, was based on his belief that it "did not serve the American people", Tillerson said in Sydney.
"It did not serve their future economic interest either," he added.
"But I think the president indicating his desire to re-examine, enter into discussions with others -- perhaps a new construct of an agreement -- indicates his recognition that the issue is still important and that he wants to stay engaged on the issue."
Tillerson, who reports have suggested was among those who counselled Trump not to scrap the deal, said last week the United States would pursue unilateral efforts to curb greenhouse gas emissions despite plans to pull out of the Paris accord.
He insisted in Sydney that his boss was "not walking away" from the issue altogether.
As well as a world outcry, Trump's decision prompted a domestic backlash, with state governors, city mayors and powerful companies already drawing up plans to meet the Paris pact's greenhouse gas emission targets.
With the United States virtually isolated on the world stage, a string of administration officials have sought to justify the decision to abandon the 195-nation Paris deal curbing global emissions.
The agreement commits signatories to efforts to reduce greenhouse gas emissions and keep the worldwide rise in temperatures below two degrees Celsius (3.6 degrees Fahrenheit) over pre-industrial times.
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