“Iran hides behind its assertion of technical compliance with the nuclear deal while it brazenly violates the other limits on its behavior,” she said. “And we have allowed them to get away with it. This must stop.”

Ms. Haley also demanded that the Council take action on what she called Iran’s “most threatening act”: ballistic missile launchings.

A Security Council resolution that put the nuclear agreement into effect calls upon Iran to refrain from ballistic missile tests but does not prohibit them. Iran has argued that its missiles are a defensive countermeasure to deter hostile neighbors, notably Israel and Saudi Arabia, both close American allies.

There was no indication that other Council members would act on Ms. Haley’s demands. China and Russia, veto-wielding members who also are parties to the Iran nuclear agreement, are strong supporters of it.

More broadly, they oppose the Trump administration’s efforts to ostracize Iran.

Iran’s ambassador to the United Nations, Gholamali Khoshroo, offered what amounted to a diametrically opposite appraisal of Iran’s behavior in his Council remarks, saying “no country has done more than Iran” in fighting Middle East terrorism, most notably in fighting the Islamic State.

“If we had hegemonic ambitions, the nuclear deal would never have been reached,” Mr. Khoshroo said. He said Mr. Trump’s approach “toward the deal and Iran run counter to all of these efforts and intend to add another crisis to the regional issues.”

Hours earlier in Tehran, Iran’s supreme leader, Ayatollah Ali Khamenei, delivered a tough denunciation of Mr. Trump’s position on the nuclear deal and his other criticisms of Iran, calling it “a waste of time to respond to such blatherings and nonsensical remarks by the foulmouthed U.S. president.”