Iran wants all ships using the Strait of Hormuz to travel only through a channel close to its shores, and has made no secret that it intends to charge fees for passage at the end of a 60-day negotiation period set in last month's memorandum.
Washington has encouraged ships to use an alternative route to the south, along the Omani coast, without coordinating with Iran.
Since last week's flare-up, Iran has declared the strait closed. The United States responded by reimposing its own blockade of Iran's ports from Wednesday, including firing at an empty tanker in the strait it said was bound for Iran. The U.S. military said it fired Hellfire missiles into the tanker's smokestack near Iran's Kharg Island after it ignored warnings.
U.S. forces say their airstrikes have hit Iranian military targets along the coast to cripple its ability to control the strait. But Iran, which can hit ships with missiles and drones from afar, says its grip does not rely on such coastal bases.
"The Americans thought that by attacking some of our bases on the southern coasts of the country, they could take control of this strategic strait," military spokesman Brigadier General Mohammad Akraminia said on Thursday.
Iran can "exert control over the Strait of Hormuz from every single point of its territory," he added.
Three U.S. officials told Reuters that the U.S. strikes could also serve as "shaping operations", giving Trump more options by targeting Iranian military capabilities that the U.S. would want to have destroyed before taking bigger steps. "This is helping set the stage, if needed," one of the officials said.
Trump has not ruled out the possibility of using ground forces, including to seize Kharg Island, site of Iran's main oil export terminal. He has repeated threats to hit Iranian power plants and bridges next week unless Tehran resumes negotiations.
Akraminia said that if Trump carried out that threat, Iran's armed forces would strike "all remaining infrastructure" across the region, and the response would be more severe, wider in scope and more destructive than previous attacks.
For now, Iran's retaliatory strikes have been focused on U.S. bases in neighbouring countries. Iran said on Thursday it had targeted U.S. bases in Kuwait and Jordan, including an air base in Jordan that Washington has upgraded in recent years into a regional headquarters.
It said the Jordanian base had been used to launch attacks on Iran, including one that struck a target in the city of Ahvaz, causing damage to a nearby children's cancer hospital that had to be evacuated.
"Our neighbours should know that providing a base to the Americans and allowing them to fire on Iranian soil is unacceptable and will not go unanswered," Iran's army said.