UNITED NATIONS — When President Trump withdrew the United States from the Iran nuclear deal in May, France’s ambassador to the United Nations lamented what he called the coming of “a new world disorder.”
America had resigned its role as “a last resort enforcer of international order,” the ambassador, François Delattre said, and there was little France or any other country could do about it.
Since then, the United States has moved still deeper into going it alone at the United Nations, withdrawing from some important agencies and defunding others.
Still, the United States remains by far the biggest single financial contributor to the global organization. But the Trump administration also has pursued what it calls an America First agenda that critics, among them close allies, say has exacerbated crises.
They also say Mr. Trump’s actions have contributed to a level of intractability in the Security Council, the most powerful United Nations body, not seen since the Cold War.
For committed internationalists like Mr. Delattre, there was some hope a year ago when Mr. Trump made his debut at the General Assembly session attended by world leaders. He alleviated the worst fears, if only briefly, when he pledged to seek changes at the United Nations that would make it a “greater force for peace and harmony in the world.”
Mr. Trump began his General Assembly agenda on Monday by participating in a panel on countering narcotics trafficking, which aides said showed his commitment to global cooperation. But few diplomats are under any illusion about Mr. Trump’s return visit this week.
He was expected to deliver an address on Tuesday heavy on state sovereignty and American interest above all, according to his ambassador, Nikki R. Haley.
In a news conference last week, Ms. Haley reprised a talking point from her first confrontational days as ambassador, when she linked America’s financial generosity around the world to support for American priorities and promised she would be “taking names” of those who did not have America’s back.
“We’re going to be generous to those that share our values, generous to those who want to work with us,” she said, “and not those that try and stop the United States, saying they hate America and are counterproductive for what we’re doing.”
That tone has been matched by action over the last year as the United States has pulled out of one United Nations body after another.
Just weeks after Mr. Trump’s first speech before the General Assembly he withdrew the United States from Unesco, the United Nations cultural organization. This summer, the United States left the Human Rights Council, revoked funding for the United Nations agency that provides education and health care to Palestinians classified as refugees, and boycotted a United Nations agreement on migration.
Mr. Trump’s decisions to quit the Paris climate accord and the Iran nuclear deal are still sources of deep bitterness, particularly among close allies. His elevation of John R. Bolton, who muses about defunding the United Nations, to national security adviser was greeted with a shudder.
At a news conference last Thursday, the United Nations secretary general, António Guterres, said that multilateralism was “under attack from many directions,” but diplomatically sidestepped a question about whether he thought Mr. Trump was a direct threat.
“I don’t like to personalize things,” he said.
Others were more blunt.
“It’s not just stepping back,” said Louis Charbonneau, the United Nations director for Human Rights Watch. “It’s an assault on the most important institutions we have for accountability and monitoring and exposing the worst abuses.”
Few would disagree about the need for some structural changes to the United Nations bureaucracy, which Mr. Trump, as president-elect, once described as a club where diplomats fraternize “and have a good time.”
When no one is in earshot, some United Nations officials are even willing to consider the possibility that the disruptions caused by the Trump administration could do some good.
But nearly two years into his presidency, Mr. Trump remains for much of the world a source of bewilderment.
Zeid Ra’ad al-Hussein, the recently retired United Nations High Commissioner for human rights, likened Mr. Trump to a bus driver “careening down a mountain road with steep cliffs on either side,” while in the back humanity hangs on for dear life.
Mr. Trump’s decision to conduct a session of the Security Council this week, which is his right as leader of the country that currently holds the body’s rotating presidency, already has been a source of anxiety and confusion.
First his administration announced that he would focus on Iran, rankling European diplomats opposed to his withdrawal from the nuclear accord, while opening the door to a face-to-face showdown between the president and Iranian leaders. Under Security Council rules, a country that is the specific subject of a meeting has the right to be represented there.
Ms. Haley had barely announced that the topic had been changed to the broader issue of nonproliferation when the president appeared to have upended her with a tweet.
“I will Chair the United Nations Security Council meeting on Iran next week!” he wrote. Administration officials sought to allay any confusion, saying that nonproliferation was the topic.
The General Assembly session has come against the backdrop of global calamities: wars in Syria and Yemen, ethnic cleansing in Myanmar, the proliferation of weapons of mass destruction and climate change. American leadership, many argue, is a prerequisite for solving each of these crises. But in case after case, critics say, American leadership is lacking.
On the mother of all conflicts, between Israel and the Palestinians, “the U.S. lost its credibility as a broker,” said Riyad H. Mansour, the Palestinian ambassador to the United Nations.
In a rebuke to the United States last year, all other Security Council members rose up to criticize Mr. Trump’s decision to move the United States embassy in Israel from Tel Aviv to Jerusalem, the disputed holy city that the Palestinians want as the capital of their future state. Ms. Haley vetoed a resolution demanding a reversal of the decision.
Ms. Haley, who has been credited by some diplomats with doing her best to moderate the president’s isolationist instincts, insists that the United States remains engaged with the world, but on its own terms.
At the news conference last week, she listed the highlights of her turn as president of the Security Council, including sessions on human rights abuses in Venezuela and Nicaragua and an initiative to improve United Nations peacekeeping.
Others credited the United States with pressuring the Security Council to adopt an arms embargo on South Sudan as well as helping to lead a campaign in recent weeks to avert a military offensive in Syria by the forces of President Bashar al-Assad and his allies, Russia and Iran.
But rights groups and other critics of administration policy say that when it comes to the United Nations, Mr. Trump and his associates have chosen mainly to disengage.
“I think Donald Trump’s rise to the presidency has made a challenging situation significantly more challenging,” said Kumi Naidoo, the secretary general of Amnesty International. “He has taken it to another level of isolation.”