Then on Sunday, when United Nations members reached agreement on a 2018-2019 budget of $5.4 billion, Ms. Haley issued a statement emphasizing the American role in achieving more than $285 million in cuts, along with hints of more reductions to come.
“We will no longer let the generosity of the American people be taken advantage of or remain unchecked,” Ms. Haley said. In future negotiations, she said, “you can be sure we’ll continue to look at ways to increase the U.N.’s efficiency while protecting our interests.”
It was certainly not the first time Ms. Haley had hinted at using America’s financial leverage to get its way at the United Nations. When she first took the job last January, she warned that “you’re going to see a change in the way we do business.”
And Secretary General António Guterres has said that some parts of the organization must become more efficient.
But the link between American largess and political sympathies at the United Nations has been a recurring theme for Mr. Trump, who once described the 72-year-old organization created after World War II as a sad social club that had squandered its potential.
Many among Mr. Trump’s base of supporters regard the organization as suspiciously anti-American. When the $285 million budget cut was reported on Monday in Breitbart News, a media group that supports Mr. Trump, reader responses were ebullient, with some arguing that America’s entire contribution should be rescinded.
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Critics of Mr. Trump’s approach to the United Nations argue that American coercion can work against the United States, by subverting respect for the agreed-upon protocol for financial contributions. They say Mr. Trump should not expect others to follow his lead just because the United States wields the biggest monetary cudgel.
“The hallmark of this administration is not paying attention to the benefits that the United States actually gets in a rule-bound system with international institutions,” Stewart Patrick, a senior fellow at the Council on Foreign Relations, said after the Jerusalem vote last Thursday. “This is not something we can treat in a purely transactional way.”
Under a formula tied to economic size and other measurements established under an article of the United Nations Charter, the United States is responsible for 22 percent of the United Nations operating budget, the largest contribution. It paid about $1.2 billion of the 2016-2017 budget of $5.4 billion.
The United States also is the largest single financial contributor, at 28.5 percent, to a separate budget for United Nations peacekeeping operations, which totals $6.8 billion in the 2017-2018 budget finalized in June.
Then, as now, Ms. Haley took credit for cuts to that budget, which she said had exceeded $500 million. “We’re only getting started,” she said at the time.
According to the United States Mission, the reductions in the budget reached on Sunday included across-the-board cuts in expenses for travel, consultants and other operating expenses. It also included tightened rules on compensation and new ways to maximize the use of United Nations headquarters in New York to reduce the need for expensive leased space.
Human rights groups reached on Monday reserved judgment on the new budget, saying they needed to see more details on how it might affect the United Nations’ ability to monitor abuses or respond to emergencies — major parts of its work.
They also did not necessarily disagree with Ms. Haley’s appraisal of the cuts. But some worried about the potential impact of future reductions.
“There’s nothing wrong with increasing efficiency and eliminating waste at the U.N.,” said Louis Charbonneau, the United Nations director at Human Rights Watch. “But it’s crucial that we don’t curtail the U.N.’s ability to monitor, investigate and expose human rights abuses or its ability to save the lives of men, women and children worldwide.”