US President Donald Trump has vowed a strong response after Iran attacked American targets in the Middle East, escalating tensions between the two sides after more than a month of relative calm.

"We're going to hit them hard," Trump said, according to a Fox News reporter who briefly spoke to him. "There will be a response," he added after Iranian attacks that came in retaliation for US strikes on an Iranian island in the Strait of Hormuz.

The exchange marked the first direct flare-up between Washington and Tehran in over a month and raised fears of renewed major hostilities.

On Sunday, the United States said it had struck Iranian rocket launchers on Larak island in the Strait of Hormuz to prevent Tehran from planting mines in the key shipping route.

Iran responded on Monday by targeting US military sites in Jordan and the United Arab Emirates, claiming it had struck American forces.

Iran's Revolutionary Guards said they fired ballistic missiles at two US air bases in Jordan, claiming to have caused "heavy damage". Jordan's army said it intercepted eight missiles without specifying their origin.

Iran also said it targeted US personnel at an air base in the UAE and shot down an American drone over Hormuz. Abu Dhabi confirmed intercepting a drone over its waters but dismissed claims that Al Minhad Air Base had been targeted as "baseless".

The latest confrontation came even as Iranian President Masoud Pezeshkian said continuing the war was not in Tehran's interests.

"We continue to strive for a path of agreement and understanding, and we believe that continuing the war is neither in our interest, nor in the interest of the region," Pezeshkian said at a Shanghai Cooperation Organisation summit in Kyrgyzstan.

He said Iran believed dialogue and cooperation were needed to prevent further insecurity and conflict.

The US-Iran tensions continue to centre on the Strait of Hormuz, which Tehran has kept closed to commercial shipping since the war began. The waterway is one of the world's most important energy shipping routes, with around one-fifth of global oil passing through it before the conflict erupted.

Diplomatic efforts to end the six-month-long conflict have so far failed to produce a final settlement despite a ceasefire agreed in April and a memorandum of understanding signed in June.

With AFP inputs