Divisions within Trump's administration have left in doubt the participation of the world's number two carbon polluter -- after China -- in the landmark 2015 agreement to limit global warming.
After months of uncertainty, Trump had appeared to be edging toward a decision.
But the White House postponed a key meeting scheduled for Tuesday that could have determined the fate of the 196-nation accord, and hours later said there would be no decision before the end of the month.
Trump will "not be making an announcement regarding that agreement until after he returns from the G7," said White House spokesman Sean Spicer Tuesday, referring to a meeting in Sicily that ends May 27.
Despite hardline pre-election rhetoric against the deal, Trump's inner circle has been tasked with providing the president with a range of policy options.
The group includes Secretary of State Rex Tillerson, White House strategist Steve Bannon, Environmental Protection Agency administrator Scott Pruitt, as well as Trump's daughter Ivanka and son-in-law Jared Kushner.
Administration officials said the crunch sit-down may now take place next week, before Trump departs for a bumper first foreign trip that will take in Saudi Arabia, Israel, the Vatican and Brussels before ending in Sicily.
"The president wants to make sure he has an opportunity to continue to meet with his team to create the best strategy for this country going forward," said Spicer.
One option said to be under consideration is full withdrawal from the Paris accord, fulfilling Trump's campaign promise to "cancel" the deal as president.
Bannon and Pruitt are said to be among those arguing for a tough line, rejecting global agreements they believe tie the hands of US industry.
Pruitt, the US government's leading environmental official, has rejected the scientific consensus that humans are the "primary contributor" to global warming.
Ivanka Trump has meanwhile become a talisman for those who believe she can be a moderating influence on her father.
But her stance on the Paris accord and her influence inside the cut-throat world of White House politics are unclear.
Full withdrawal would roil Washington's allies and seriously undermine global efforts to limit carbon emissions, which the vast majority of experts say are changing the climate in dangerous ways.
- Kyoto, take two? -
For US allies, Trump's wavering has uncomfortable echoes of president George W. Bush's decision to withdraw from the 1992 Kyoto Protocol.
That move scuttled a carefully worked global compromise and effectively delayed climate action by two decades.
It would also wreck Trump's careful diplomacy with China, which the White House wants on-side to tackle North Korea's nuclear and ballistic missile programs.
The core of the Paris deal was an agreement between Chinese President Xi Jinping and then US president Barack Obama. Both men have pressed Trump to stay on board.
"It's important that big countries that are big emitters like the US and China... lead the way," Obama told a conference Tuesday in Milan, in one of his first public appearances since leaving office.
- Middle road -
Another possible option for Trump, according to officials, is to remain within the agreement, but rework US emissions targets.
Obama set targets to reduce emissions by 26-28 percent below 2005 levels by 2025.
Sue Biniaz, a former State Department legal adviser who supports the accord, said Trump does not need to make a binary choice between leaving or staying.
"It is clear from the agreement that if you do change your target, you are encouraged to change it in a more ambitious direction," she said.
"But it is equally clear that you are not legally prohibited from changing it in any direction that you choose."
The US wavering left UN climate negotiators -- who happened to be gathered in Bonn to thrash out the nuts-and-bolts of the deal -- in limbo.
They are gathered to start designing a "rulebook" for implementing the global deal to limit average global warming to two degrees Celsius (3.6 degrees Fahrenheit) over pre-industrial levels.
This is the ceiling at which scientists say the planet can avoid worst-case-scenario climate change impacts -- rising seas, harsher droughts, more intense storms, disease-spread and conflict over dwindling natural resources.
Speaker after speaker in Bonn reiterated the deal must not be "renegotiated" -- a proposal of Trump's Energy Secretary Rick Perry.
"It is definitely the elephant in the room," a member of one national delegation told AFP on Tuesday.
Some fear a US U-turn would dampen enthusiasm among other signatories to increase their emissions-cutting targets.
This is key, as current pledges place the world on track for warming much higher than the two degrees Celsius ceiling.
