Iranian foreign ministry spokesman Esmaeil Baghaei meanwhile stressed that the situation in the disputed strait will not return to its pre-war status, according to broadcaster Press TV.
Iran was acting in its own interests and would not change its decisions based on threats or intimidation, Baghaei said.
However, an agreement with Oman on a new shipping route did not mean the Strait of Hormuz would be opened or closed, the spokesman said, according to state broadcaster IRIB.
The United States and Iran agreed on a framework deal in mid-June.
Under the agreement, Iran is to reach an accord with Oman, in co-ordination with the strait's other coastal states, on the future management of the waterway.
No details of what a possible agreement could entail were available on Sunday.
The dispute over transit rights through a key route for oil, gas and fertiliser is considered one of the main triggers for the recent escalation in the military conflict between the US and Iran.
US President Donald Trump said the United States would hold off on a new attack on Iran as long as a deal can be reached quickly to halt Iran's nuclear ambitions and reopen the Strait of Hormuz.
Trump said late on Saturday on his Truth Social platform that Iran and other Middle Eastern countries had asked for time to complete a deal that would lead to "the Immediate, Complete and Total" reopening of the vital strait and "an end to Iran's nuclear threat".
He did not name the countries in the post, which followed a call with Crown Prince Mohammed bin Salman of Saudi Arabia.
"Based on this request, I have agreed, for the future benefit of the WORLD and, likewise, the survival of a successful and prosperous Iran, to cancel the attack, subject to being able to rapidly make a DEAL," Trump wrote.
Israel "joins me in this commitment," he said.
Iranian defence minister Brigadier General Majid Ebn Al-Reza said on X that the country was "neither surprised nor passive" following Trump's announcement and said Iran continues to remain alert in the face of concrete threats from the US.
Last month Iran publicly rejected an Omani proposal, backed by Gulf states, to manage the strait they share.
People familiar with the matter had told Reuters the plan included the collection of voluntary fees for using the strait.
with Reuters and AP
