(CNN) In five months in office, UN Secretary-General António Guterres, has so far publicly avoided challenging new US President Donald Trump.

But on Tuesday, he threw the equivalent of a last-minute "Hail Mary" pass during a speech at New York University -- making the case for the US to remain committed to the Paris climate accord in terms that he hoped would change Trump's mind, by warning of a drop in the US's global influence if it pulls out of the agreement.

Guterres did not mention Trump by name in his speech, although a western diplomat noted to CNN that "the speech was aimed at the Trump administration." But Guterres used a physics comparison to explain what would happen if the US did, in fact, leave the Paris agreement.

"It's proven now that vacuum can exist in physics. But vacuum cannot exist in geostrategic dimensions," he said. "Which means that if one country decides not to be present -- and I'm talking about countries with an important global reach like the United States or China -- if one country decides to leave a void, I can guarantee someone else will occupy it."

Guterres said in a speech Tuesday that he believes climate change can't be denied, and added: "It is absolutely essential that the world implements the Paris Agreement."

In the question-and-answer session that followed, Guterres stated plainly that it's important for the US to not leave the Paris agreement. He added that he hoped that despite Trump's choice, state and local governments and businesses would jump in to help in the climate fight.

"When you disagree with someone, you try to convince that person, no?" he said. "It's the same with administrations. We are engaging with the American administration. We believe it would be important for the US not to leave the Paris agreement. But even if the US government decides to leave the Paris agreement, it's very important for the US societies as a whole, for the cities, the states, the companies, the business to remain engaged with the Paris agreement -- so it is very clear that governments are not everything."

The UN tweeted Guterres' remarks Wednesday in the wake of Trump's decision.

"Climate change is undeniable

Climate action is unstoppable

Climate solutions provide opportunities that are unmatchable.

-@antonioguterres," the tweet read.

Climate change is undeniable



Climate action is unstoppable



Climate solutions provide opportunities that are unmatchable.

-@antonioguterres https://t.co/a8O14NCLUc — United Nations (@UN) May 31, 2017

Guterres has had to tread carefully when it comes to the US, the largest financial donor to the UN. Trump and UN Ambassador Nikki Haley are demanding budget cuts and personnel reductions. But his comments Tuesday at NYU were some of his boldest to date.

The speech was a "calculated gamble," Richard Gowan, a fellow at NYU's Center on International Cooperation, said, adding that Trump may "react badly" to even a limited challenge from the UN, which he views with suspicion.

"Guterres may calculate that Trump cannot face the idea of a drop in US influence, even if he doesn't care about carbon emissions," Gowan said. "This speech was both a plea and a threat to Trump. Guterres pressed the case for the US to stick with the Paris deal, but also left no doubt that China can and will replace America as the global leader in the fight against climate change."

JUST WATCHED Graham to Trump: Stay in Paris climate deal Replay More Videos ... MUST WATCH Graham to Trump: Stay in Paris climate deal 01:01

As Guterres phrased it: "If any government doubts the global will and the need for this accord, that is reason for all other to unite even stronger and stay the course." He added that if leaders "only look at polls, sooner or later they will lose an election and have no legacy. ... It's better to lose an election than all ideals."

"We need political leadership," he said.

He explained that "the real danger is not the threat to one's economy that comes from acting. It is, instead, the risk to one's economy by failing to act."

Trump tweeted after he left the G-7 summit in Europe that he planned to make a decision on the Paris accord "this week," and he did not agree to sign a G-7 statement to uphold the climate agreements' carbon reduction commitments.

Asked if Guterres was trying to send a message to Trump, his spokesman, Stéphane Dujarric, said: "It was important for the secretary general to clearly lay out his vision for moving forward on confronting climate change, an overriding global challenge that we must all confront collectively."

The former Portuguese prime minister said he's always ready to discuss the climate-change issue.

He told the NYU audience: "let me also stress that my door is open to all who wish to discuss the way forward, even those who might hold divergent perspectives. The climate conversation should cease to be a shouting match."

Guterres has met Trump in person just once -- at the White House for about 15 minutes.

Reaction pours in

In the wake of Trump's announcement Wednesday, Ronald Jumeau, Seychelles' representative to the UN, said it was now incumbent on the nations left in the Paris agreement to review "what more do we have to do to step up, what needs to be done."

"How are we going to step up so that it brings benefits to it all, through business, through jobs, through healthier lifestyles and so that people not in the room can hear what's happening and say, 'I think I should be in the room rather than out,'" Jumeau said.

Referring to Trump, he added, "He's a president who's been elected democratically. It's his right to do that, whatever he wants to do. We are staying in the room."

Olof Skoog, Sweden's ambassador to the UN, said Wednesday that the US pulling out "would be a disappointment to the rest of the world since it's such an important agreement. It flies in the face of friendly European countries who made pleas to the US last week in Europe."

He added, "It would hurt America's interests in other multilateral negotiations and work in the United Nations."