The United States and Iran exchanged attacks for the first time in a month overnight on Monday, underscoring how a war that President Trump had promised would be over quickly has repeatedly frustrated his attempts to end it.

The U.S. military said on Sunday that its forces had bombarded Iranian troops on Larak Island that were preparing to launch rockets armed with mines into the Strait of Hormuz, the vital shipping corridor for oil and gas that Iran has blockaded. The Iranian foreign ministry said several people were killed and wounded, without providing specifics.

Iran’s Islamic Revolutionary Guards Corps said it retaliated by firing at bases in Jordan and the United Arab Emirates that host U.S. military personnel. The Jordanian authorities said that they had intercepted eight missiles that entered their airspace, while the Emirati military said it had “responded to” a drone coming from Iran. There were no reports of any damage or casualties.

The exchange of fire broke a tense monthlong calm that had prevailed after Mr. Trump pulled back from the brink of a renewed full-blown war, following concerns over dwindling U.S. munition stockpiles and calls for restraint from Gulf allies like Saudi Arabia.

Even as the fighting ebbed, there was little evidence of a durable solution to the war that Mr. Trump began in late February alongside Israel. A short-lived “memorandum of understanding” between Iran and the United States broke down only a few weeks after it was signed in late June.