Iran still wants to maintain control over the Strait of Hormuz, which is unacceptable for the US - Rubio

U.S. Secretary of State Marco Rubio stated that the U.S. will not tolerate Iran deciding which vessels may pass through the strait or allowing the collection of Iranian duties. This was reported by Bloomberg, according to UNN. 

The U.S. cannot tolerate Iran continuing to decide which vessels can pass through the strait or allowing any Iranian fees. If by opening the straits they mean: "Yes, the straits are open if you coordinate with Iran, get our permission, otherwise we will blow you up and you pay us" — that is not opening the straits. They cannot normalize, and we cannot tolerate their attempts to normalize a system in which the Iranians decide who can use an international waterway and how much you must pay them to use it, 

As the publication notes, these comments came after media reports that Iran had provided the U.S. with a new proposal to reopen the Strait of Hormuz and end the war by striking a deal that would postpone more complex negotiations regarding the country's nuclear program. Trump and other U.S. officials have stated that Iran's nuclear ambitions were the primary reason for the start of the U.S. and Israeli war against Tehran.

The Strait of Hormuz, through which a fifth of the world's oil and liquefied natural gas exports are typically transported, has been effectively closed since the U.S. and Israeli attack on Tehran in late February. Although Iranian threats initially closed the strait, the U.S. is now also enforcing a naval blockade to prevent Iran-linked ships from sailing through the Strait of Hormuz.

While the truce has mostly held since early April, the closure of the strait has led to a sharp increase in global energy prices. The waterway, which functioned normally before the war, has become one of the main stumbling blocks in the U.S.-Iran negotiations mediated by Pakistan, with the previous round of talks in Islamabad ending without any agreement.

As a reminder, 

The U.S. announced the start of an operation to search for and neutralize mines in the Strait of Hormuz to restore safe shipping through the key oil route.