“It appears that he left out the anti-U. N. rhetoric he was so fond of during the campaign and instead recognized the potential of the U.N. to be involved in solving global crises and with an important role to play,” said Rachel Stohl, a scholar at the Stimson Center, a nonpartisan research organization. By Tuesday, she said, “I would expect him to play to his base a bit and call for greater action with regards to Iran and North Korea.”
While he has made a few international trips as president, this is Mr. Trump’s first experience with such a varying collection of world leaders — with vastly different issues — all at once. His first overseas trip started off smoothly with largely on-message stops in Saudi Arabia and Israel, only to generate a furor later in the week when he went to Europe and refused to explicitly endorse NATO’s commitment to mutual defense.
“The president is not one to pull punches,” said Suzanne Nossel, executive director of PEN America, a human rights group, and a former State Department official under Presidents Bill Clinton and Barack Obama.
Ms. Nossel said Mr. Trump seemed to be “at an inflection point with his political base” and might feel pressure to lash out. “I hope he resists the temptation to treat the U.N. as a punching bag in order to please conservatives as they witness him waver on other hot-button issues,” she said.
The president started his day meeting with counterparts about overhauling the United Nations. He complained that its spending and staff had grown enormously but that “we are not seeing the results in line with this investment.”
Still, his criticism was mild compared with the bombast of the past. As recently as December, he dismissed the United Nations as “just a club for people to get together, talk and have a good time” and as president he had yet to meet with Mr. Guterres.
On Monday, he commended the secretary general for seeking “to focus more on people and less on bureaucracy.” He added: “We seek a United Nations that regains the trust of the people around the world. In order to achieve this, the United Nations must hold every level of management accountable, protect whistle-blowers and focus on results rather than on process.”
Mr. Trump said any reform should ensure that no member “shoulders a disproportionate share of the burden, and that’s militarily or financially,” a nod to conservatives who bristle at the United Nations costs borne by the United States. Mr. Trump said nothing about whether he would pursue his proposal to radically cut American funding for the organization.
The event, organized by Mr. Trump’s envoy to the United Nations, Nikki R. Haley, was part of a still-vague effort to revamp the United Nations system. Her blueprint contains proposals that have been circulated for years. Its significance lies in its support for the United Nations’ very existence rather than a bludgeoning of it, and Ms. Haley said 128 countries had backed it so far.
“It was a good day for Nikki Haley” and Lt. Gen. H. R. McMaster, the president’s national security adviser, said Bruce Jones, a scholar at the Brookings Institution. “They pulled off an effective alignment between Trump’s priority — namely better burden sharing — and U.N. reform.”
Mr. Jones said it was also “a good day” for Mr. Guterres “as the threatened rift between Trump and U.N. was bridged,” then noted: “Tomorrow comes the pressure — on Iran and North Korea.”
Mr. Trump later met with Prime Minister Benjamin Netanyahu of Israel, in the first of a string of sessions he will conduct with counterparts during four days in New York. Mr. Netanyahu pressed Mr. Trump to either revise the Iran nuclear agreement negotiated by Mr. Obama or scrap it.
Asked by reporters if he would withdraw, Mr. Trump said: “You’ll see very soon. You’ll be seeing very soon.” He added: “We’re talking about it constantly. Constantly.”
The president later met with President Emmanuel Macron of France and the two called each other by their first names as they traded warm words and recalled Mr. Trump’s visit to a Bastille Day military parade in Paris in July. They saved disagreement over the climate accord until the cameras were off. Mr. Trump then hosted a dinner with Latin American leaders, where he assailed Venezuela’s president, Nicolás Maduro, for “stealing power” from the people and wrecking the economy.
“Our goal must be to help them and restore their democracy,” he said.
Mr. Trump’s main message will come on Tuesday when he addresses the General Assembly. Aides have said he will seek to explain how his America First approach squares with a robust international body with the argument that nations that pursue their own interests can come together for common causes.
The address will offer challenges for a president whose most animated public speeches feed off a lively crowd response. In the setting of the United Nations, where words are translated into multiple languages to an audience from varied cultures, jokes and casual references generally do not work.
President George W. Bush often said it was “like speaking to the wax museum — no one moves.” Tony Blair, the former British prime minister, told a forum hosted by the Concordia Summit on Monday that his United Nations speeches were the toughest of his career.
Mr. Trump’s attempt at a joke on Monday seemed to elude some of the foreign leaders in the room. He cited his days as a real estate developer and his decision to build Trump World Tower opposite the organization’s headquarters, a building where several foreign diplomats working at the United Nations have their official residences.
“I actually saw great potential right across the street, to be honest with you,” he said, “and it was only for the reason that the United Nations was here that that turned out to be such a successful project.”