The strikes were the latest in a cycle of attacks and counter-attacks as Iran seeks to assert control over shipping through the strait.
However, the barrage marked an escalation in pace and range.
The strikes extended to Qatar, a mediator in ceasefire talks that had not come under attack since April, while the United Arab Emirates, which had not been targeted since early May, said its air defences had engaged missiles and drones from Iran.
Iranian media said there had been missile attacks and explosions around the port of Bandar Abbas, home to military facilities on the strait, and nearby Qeshm island on Sunday afternoon as the US reportedly launched another round of attacks.
The state-run IRNA news agency cited the governor of Qeshm island as saying projectiles had been fired at military targets, with no casualties.
The renewed violence casts further doubt on the future of an interim US-Iranian agreement signed last month that aimed to reopen the strait and end the war after a further 60 days of negotiations.
In the past week, US President Donald Trump has said he considers the ceasefire over while leaving the door open to more talks.
The war that the US and Israel launched against Iran on February 28 has destabilised the Gulf, where Iran has struck countries hosting US bases.
Iran's effective blockade of the strait has driven energy prices higher, fuelling global inflation.
Higher prices, especially for petrol, are politically sensitive for Trump ahead of November's congressional elections.
Iranian officials have sought to establish a permanent system for collecting fees in the strait, which carried one-fifth of the world's oil and liquefied natural gas shipments before the war, and has warned vessels not to sail without its authorisation.
It said late on Saturday it had closed the waterway after firing a warning shot that struck a vessel travelling on an unauthorised route.
On Sunday, it said it had disabled a second vessel.
India said one of its citizens was missing after an attack on the container ship GFS Galaxy off the coast of Oman.
Oman said 23 crew members had been rescued.
Qatar advised all vessels, including leisure boats, fishing boats and jet skis, to suspend activities.
Iran's recently created Persian Gulf Strait Authority said on Sunday that passage through the strait was not currently possible due to "recent illegal movements of the United States military forces in the region".
Permits would be issued "as soon as stability and calm are restored," it said.
The US, which revoked the licence authorising the sale of Iranian crude on Tuesday following earlier attacks on shipping, said its forces were positioned to safeguard freedom of navigation despite what it described as "aggression, harassment, threats, and arbitrary declarations" from Iran.
"Iran does not control the strait. Traffic is flowing," it said.
The US navy-led Joint Maritime Information Center reiterated guidance that, despite a severe security threat, an "expanded" southern route near Oman was available for two-way traffic.
On Saturday, US Central Command said US forces had hit 140 Iranian military targets and that more than 300 had been struck over three nights this week "to degrade Iran's ability to attack civilian mariners and commercial vessels freely transiting the strait".
Iranian state media reported explosions in several port cities and said an Iranian army officer had been killed.
In response, Iran's Revolutionary Guards said they had destroyed a command-and-control centre and drone hangars in US ally Jordan, targeted a US radar site in Kuwait, attacked US aircraft carrier support and refuelling platforms in Oman and destroyed a jet maintenance centre and command facility in Qatar.
with AP
