President Donald Trump has said the US could "conceivably" return to the 2015 Paris climate accord if an agreement treated America more fairly.
He said it "was a bad deal for the US", repeating comments made when he announced the US withdrawal last June.
But he said he had no problem with the accord itself.
A US pull-out will make the US in effect the only country not to be part of the accord. The announcement sparked global anger.
Some critics have called it an abdication of US leadership on a key global challenge.
The Paris agreement commits countries to keeping the rise in global temperatures "well below" 2C more than pre-industrial levels and aiming for a tighter limit of 1.5C.
In a separate development on Wednesday, New York City announced plans to sell off $5bn (£3.7bn) in fossil fuel investments from its $189bn public pension funds over the next five years.
The city authorities also filed a multibillion dollar lawsuit against five major oil companies, seeking damages for "contributions to global warming".
New York City said the lawsuit against BP, Chevron, ConocoPhillips, Exxon Mobil and Royal Dutch Shell would help fund protection against climate change.
The lawsuit follows similar recent moves by a number of cities in California, reports BBC.