Iran’s state broadcaster published the statement by the council’s secretary, Mohammad Bagher Zolghadr, who is also a commander in the powerful Revolutionary Guard.
The US must never threaten Iran again, the statement said, and must permanently end the war with Iran and its armed allies in the region.
The US must lift the naval blockade of Iranian ports and withdraw its military from the area.
It also must “completely compensate” Iran for war damage, lift sanctions and “unconditionally” release frozen assets.
There was no immediate response from the US, which has wanted an acceptable deal first on the strait before ending the blockade.
Iran earlier said it was close to reaching a deal with Oman to manage the strait, which runs between the two countries.
Oman, a mediator Gulf Arab country which has said relatively little on the talks, said in a statement on Saturday that the discussions were ongoing “in a positive and constructive atmosphere” and condemned attacks on ships on the strait.
Also on Saturday, vessel owned by Abu Dhabi’s state-owned ADNOC oil and gas company was attacked while transiting the Strait of Hormuz, Emirati authorities said.
The Foreign Ministry said Iran fired the missile as part of attacks on commercial shipping.
ADNOC said in a statement that there were no casualties following the attack.
The company said over a dozen of its vessels have been attacked by missiles and drones while passing through the strait since the US and Israel launched the war on Iran in February.
One crew member has been killed and 20 others wounded, it said.
ADNOC did not elaborate on where the attack took place nor on any damage.
Later, the United Kingdom Maritime Trade Operations Centre said a vessel east of the town of Khasab, Oman, had been struck by a projectile that caused a fire that was put out, with the vessel and crew safe.
It was not immediately clear whether this was the ADNOC incident.
Iran and Oman, on the other side of the strait, have been discussing a deal to manage the waterway, which had been considered an international one before the war.
The attacks were in response to the Houthis’ recent strikes in central and eastern Yemen.
Colonel Majed al-Nazili, spokesperson for Yemen’s military, said the attacks targeted the rebels’ “sites and capabilities” on multiple front lines, without elaborating.
The escalation between the Houthis and Yemen’s internationally recognised government and its backer, a Saudi-supported coalition, threatens to reignite Yemen’s civil war following a 2022 truce.
On Friday, United Nations envoy Hans Grundberg urged the parties to exercise restraint, saying that “Yemen today faces a greater risk of renewed large-scale conflict than at any point since the UN-brokered truce of April 2022″.