In a statement, US Central Command said it had begun "a new wave of strikes" aimed at "degrading" Iran's ability to attack commercial vessels in the strait's vital shipping lanes.
Iran responded by launching an attack targeting Bahrain, the home of the US Navy's 5th Fleet.
The strikes are part of an escalating cycle of attacks between the US and Iran after an interim ceasefire agreement signed a month ago unravelled, deepening a struggle for control over the Strait of Hormuz that has disrupted energy supplies and stoked fears of global inflation.
Both sides have targeted civilian infrastructure relied on by millions of people.
Iran's semi-official Tasnim news agency said US missiles struck several Iranian cities early on Monday.
Explosions were heard in Tabriz, Chabahar, Konarak, Bandar Mahshahr and Bandar Imam Khomeini, according to Tasnim.
US Secretary of State Marco Rubio said the United States would continue to target Iran while it attacked global commercial shipping.
"As long as Iran insists on controlling an international waterway, we're gonna have to respond to that. The United States always remains open to a diplomatic solution," Rubio said.
The Islamic Revolutionary Guard Corps announced a surprise strike against "the enemy's special operations headquarters in Syria's Al-Tanf area".
The Revolutionary Guards also said they targeted US aircraft at Jordan's Aqaba airport with ballistic missiles.
Iran earlier conducted a drone attack on US military assets and equipment at Kuwait's Al-Adiri camp and Ali Al Salem Air Base, Iranian state TV reported early on Sunday.
Kuwait's government said a desalination plant was attacked for the second day running, causing a fire, in what it called a direct strike on vital civilian infrastructure.
Concerns about the flow of energy supplies through the Strait of Hormuz have persisted since the United States and Iran resumed open hostilities after accusing each other of repeatedly violating a ceasefire deal.
The United Kingdom Maritime Trade Operations said late on Sunday that it received a report that a vessel was on fire not far from the Omani coast, although it had not verified a cause.
The Revolutionary Guards said on Monday that two oil tankers had exploded and been immobilised after attempting to transit what it described as an unsafe southern route through Hormuz, alleging the vessels had been encouraged by the US military to use the passage.
The statement gave no details on the vessels' names, flags, crews or any casualties.
The Guards said the waterway would remain unsafe as long as what it called US "aggression" in the region continued, warning that "this passage will not be safe for the transit of petrochemical products, nor even a single drop of oil and gas".
Four vessels made the transit through Hormuz on Sunday, down from eight the previous day, LSEG data showed.
At least three oil products' tankers and one Very Large Crude Carrier have entered the strait since Friday to load oil, the data showed.
Oil prices rose two per cent to more than $US90 ($A129) a barrel on Monday.
In the latest American casualty reported in the war, the US military said a service member was killed on Saturday in northern Iraq, where the US has military bases, during a controlled detonation of what Central Command called unexploded ordnance on a downed Iranian attack drone.
The US military said earlier that two service personnel died in Jordan and that a third was missing in action. On Sunday, Central Command said that "unidentified remains" had been found at the site of Friday's attack and that "an examination process to verify the remains is ongoing".
"We hit them very hard again tonight," US President Donald Trump said.
"And we did that in honour of the" soldiers killed, he said.
The latest casualty announcements brought the total number of US military personnel killed since the war began to 17, with more than 420 others wounded.
The conflict, which began when the US and Israel attacked Iran on February 28, seeking to disable Tehran's nuclear and missile programs and weaken its regional proxies, has killed thousands of people, mostly in Iran and Lebanon.
with AP
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