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.

Anwar Gargash, a senior Emirati official, lamented on Monday that the June cease-fire had “failed to outline a practical and acceptable road map” for ending the conflict. He called for a new agreement that would return the Strait of Hormuz to its prewar status, although he did not say what that would look like.

“The state of neither war nor peace cannot be a sustainable solution,” Mr. Gargash wrote on social media.

The United States and Iran are now in an economic battle of wills centered around control of the Strait of Hormuz, which Iran has used to throttle global energy markets since the war began.

Iran has fired on ships passing through the waterway, severely curbing the ability of U.S. allies to export oil and gas. Iranian leaders have demanded steep and immediate concessions in exchange for reopening the strait, which U.S. officials have rejected as a nonstarter.

The Trump administration has sought to squeeze Tehran economically by enforcing a naval blockade on Iranian ports, imposing heightened sanctions on Tehran and threatening to impose similar penalties on countries that trade with Iranian institutions.

U.S. forces have also quietly worked to guide ships through the southern waters of the Strait of Hormuz near Oman.

Adm. Brad Cooper, the head of the U.S. military’s Central Command, said this week that Iranian mines had successfully been cleared from the waterway’s international shipping lanes. There has been an uptick in oil tankers successfully making the crossing, but the route remains perilous. At least two seafarers have been killed in the past two weeks, and another is missing.

Vivian Nereim and Sanam Mahoozi contributed reporting.