Iran Foreign Minister Abbas Araghchi says his nation has offered a deal to the US that would reopen the Strait of Hormuz within a week.
But US President Donald Trump has already rejected the idea, according to the Wall Street Journal, renaming the waterway "Trump Strait" on his Truth Social feed.
Iran wants the memorandum of understanding signed in June to form the basis of any future peace agreements with the US and Israel.
Iran has proposed a deal to the United States that would see the Strait of Hormuz reopened within a week, according to its Foreign Minister Abbas Araghchi.
Mr Araghchi said the plan was delivered to the US via Qatar, and revisited parts of the memorandum of understanding (MOU) signed in June.
"The choice now rests with the United States," he said, adding that it could be done "if the necessary conditions are met".
However, within hours of his comments, The Wall Street Journal reported that Mr Trump had rejected the proposal, citing US officials familiar with the matter.
The report noted that the 80-year-old president was sceptical that Tehran would meet his demands and added he saw a renewed bombing campaign as likely.
Mr Trump also posted an image to his Truth Social platform of a map showing the Strait of Hormuz circled and labelled "Trump Strait".
Hossein Mohebi, a spokesperson for the Revolutionary Guard, was quoted by Tasnim news agency as saying: "We will not cease punishing the US until Iran's seven conditions are met."
Iran's plan calls for a cessation of all hostilities in the Middle East for seven days, including in Lebanon, according to Mr Araghchi.
The MOU, signed with the US earlier this year, calls for the release of frozen Iranian assets estimated to be worth at least $US12 billion ($17 billion), as well as the lifting of sanctions on Iranian oil and an end to the US naval blockade of Iran.
On the seventh day of the truce, Iran would reopen Hormuz.
Iran President Masoud Pezeshkian told US broadcaster CBS that the "process will begin from the very day they accept it".
"We had previously reached an agreement based on the MOU that was signed in Pakistan," he said.
"If the United States agrees to proceed in that way, everything will return to the way it was before.
Washington and Tehran signed a memorandum of understanding in June that aimed to end the war, reopen the strait and launch talks on Iran's nuclear program.
But the deal broke down shortly afterwards when Iran fired on commercial ships in Hormuz that it accused of deviating from its approved route through the waterway.
Iran requires ships to obtain authorisation before passage, citing security and sovereignty reasons.
Ships that refuse to comply are regularly targeted, while the US sporadically bombs Iranian coastal areas in retaliation.