The conditions included ending the war in the region, he said.
Rezaei said Iran had agreed with Oman on a corridor for shipping through the strait, with parts lying in Omani and Iranian waters.
Ships would transit through a designated central channel if the United States met Iran's conditions, he said through an interpreter in an al-Manar TV interview.
Earlier on Thursday, President Donald Trump said the United States was not talking with Iran and instead focusing on punishing it economically.
"We don't want to speak to them. We're not looking to meet or anything," Trump told reporters in the Oval Office.
Earlier in the day, White House Press Secretary Karoline Leavitt said the US economic campaign would continue until Iran decides to negotiate meaningfully.
"Now we have Operation Economic Outcast to destroy their economy," Leavitt told Fox News.
"No negotiations are happening right now, and this will continue until the president feels that maybe they come to the table in a meaningful way ... He of course continues to retain all options on the table."
US Treasury Secretary Scott Bessent warned countries on Monday to cut their financial ties with Iran or face secondary sanctions as part of what had been billed as "Economic D-Day" but the Treasury Department stopped short of actually imposing penalties.
When asked on Thursday if he would punish Russia for continuing to do business with Iran, Trump responded: "It depends. So far, I think Russia's behaved quite well, having to do with the Strait of Hormuz, and you have to understand: for everything they do, we do also. You know, somebody was saying about China. What about China? We hear they're spying. We spy on them too."
Then when asked if he would sanction Chinese banks for doing business with Iran, Trump said: "Who said I'm not? You don't know if I'm doing it ... I don't have to announce everything, do I?".
Qatar's Prime Minister Mohammed bin Abdulrahman al-Thani, who is also his country's foreign minister, visited Tehran on Thursday for meetings with Iran's Foreign Minister Abbas Araqchi, President Masoud Pezeshkian and chief negotiator Mohammad Bagher Ghalibaf.
Al Thani's trip marked the third high-level diplomatic visit within a few days.
On Monday, a delegation led by the Pakistani chief of the General Staff, Asim Munir, was in Tehran and held talks with the Iranian leadership.
This was followed on Tuesday by Oman's Foreign Minister Badr al-Busaidi.
Pakistan and Oman, in particular, have recently been mediating between Iran and the US.
with DPA
