The fresh volleys of missiles and drones came after US President Donald Trump launched a new effort to get stranded tankers and other ships through the strait.
The vital energy-trade chokepoint has been virtually closed since the US and Israel began attacks on Iran in February, a war that has killed thousands of people across the region.
Before Monday was out, several merchant ships in the Gulf reported explosions or fires, the US said it had destroyed six small Iranian military boats, and an oil port in the United Arab Emirates, which hosts a large American military base, was set ablaze by Iranian missiles.
Trump gave scant details about his new effort, which he called "Project Freedom", to help stuck ships travel through the strait when he announced it on social media on Sunday, US time.
That was two days after a legal deadline under US law had passed for him to get authorisation from Congress for the war.
Trump told Congress the war was "terminated" and the deadline was moot, a claim disputed by some lawmakers.
It was the first apparent attempt to use military force since April's ceasefire announcement to unblock the world's most important energy shipping route, which Iran's Islamic Revolutionary Guard Corps has said can only happen with its permission.
Iran's Foreign Minister Abbas Araqchi said Monday's events showed there was no military solution to the crisis.
He said peace talks were progressing with Pakistan's mediation while warning the US and the UAE against being drawn into a "quagmire by ill-wishers".
"Project Freedom is Project Deadlock," he wrote on social media.
Nonetheless, the US military said two American merchant ships made it through the strait, without saying when, with the support of navy guided-missile destroyers.
While Iran denied any crossings had taken place in recent hours, shipping giant Maersk said the Alliance Fairfax, a US-flagged ship, exited the Gulf via the Strait of Hormuz accompanied by the military on Monday.
The commander of US forces in the region said his fleet had destroyed six small Iranian boats, which Iran also denied.
Admiral Brad Cooper said he "strongly advised" Iranian forces to keep clear of US military assets carrying out the mission.
Iranian authorities released a map of what they said was an expanded sea area now under their control, extending far beyond the strait to include long stretches of the UAE's coastline.
South Korea reported one of its merchant ships, HMM Namu, in the strait suffered an explosion and fire in its engine room, though no one aboard was hurt, and a spokesman said it was unclear if the fire was caused by an attack or originated internally.
The British maritime security agency UKMTO reported two ships had been hit off the coast of the UAE, and the Emirati oil company ADNOC said one of its empty oil tankers was hit by Iranian drones.
After reported drone and missile attacks inside the UAE throughout the day, including one that caused a fire at Fujairah, an important oil port, the UAE said Iranian attacks marked a serious escalation and it reserved the right to respond.
Iran's state television network said military officials had confirmed they attacked the UAE in response to the "US military's adventurism".
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