The agreement has been criticised as far too cautious to hold back the rise in temperatures by more than a fraction of what is needed - but its defenders say its enrolment of nearly all the world's governments makes it crucial.
NY and California have already pledged to combat climate change without the Trump administration's support.
The House Democratic leader, Rep. Nancy Pelosi of California, referred to it as "a stunning abdication of American leadership and a grave threat to our planet's future".
Word of Trump's expected decision comes a day after the president met with Scott Pruitt, the administrator of the Environmental Protection Agency.
But Trump said the agreement disadvantaged the U.S.
She says in a statement that the landmark accord "honors our collective moral responsibility to leave future generations with a planet that is clean, healthy and sustainable".
If this language frustrates Trump enough, he could opt to withdraw from the more foundational UN Framework Convention on Climate Change, which laid the groundwork for the Paris deal and was signed by President George H.W. Bush and ratified by the Senate in the early 1990s. "Make America great again!", Trump said.
Judy Wakhungu, Kenya's cabinet secretary for environment and natural resources, said her government would be "very disappointed" by a US withdrawal and hoped it could be reversed.
Finnish Prime Minister Juha Sipila (JOO'-hah SEE'-pah-lah) says climate change won't be reversed "by closing your eyes". He calls the expected withdrawal "a big setback".
Guterres underscored that the science behind climate change "is beyond doubt".
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Trump's chief economic adviser, Gary Cohn, has discussed the possibility of changing the USA carbon reduction targets instead of pulling out of the deal completely.
Trump, who has previously called global warming a hoax, refused to endorse the landmark climate change accord at a summit of the G7 group of wealthy nations on Saturday (27 May), saying he needed more time to decide. "And climate solutions provide opportunities that are unmatchable", he said.
Trump has repeatedly expressed doubts about climate change, at times calling it a hoax to weaken U.S. industry.
"If someone leaves a void, I guarantee someone will fill it", said Guterres, who went on to explain what consequences such an exit could have for the US.
"I will be announcing my decision on the Paris Accord over the next few days", Trump tweeted Wednesday amid media reports that a withdrawal was looming. "AGAIN!" the U.S. leader said in a tweet late Wednesday, punctuating the post with his populist campaign slogan. Speaking to reporters on Thursday, a spokesman for President Vladimir Putin said Russian Federation "thinks highly" of the accords and sees no alternative to it. Spokesman Dmitry Peskov added that its implementation will not be as effective "without the key signatories".
In television interviews the morning after Trump's announcement, Vice President Mike Pence and Kellyanne Conway, a senior White House aide, defended Trump's decision as a reassertion of America's sovereignty.
Trump promised during his 2016 campaign that he'd withdraw the USA from the deal.
On Twitter, Trump teased the announcement of his decision as imminent this week.
At home, the U.S. Conference of Mayors strongly opposed the decision and said the nation's mayors will continue efforts to reduce greenhouse gas emissions blamed for global warming.
Donald Trump will announce this week whether the USA will remain in the Paris Agreement - the world's first comprehensive accord of its kind - after previously threatening to pull out.