Iran presented a proposal during the UN General Assembly under which the waterway could be reopened and normal maritime passage restored within seven days if the conditions were met, with the US replying to this proposal last week via Qatari intermediaries.
"The position of the Islamic Republic of Iran is completely clear and firm, and the Strait of Hormuz will not be opened until our seven conditions, based on the Islamabad Memorandum of Understanding, are met," Qalibaf, who is Iran's top negotiator, said.
He said Washington "must understand that the period of dragging out the (diplomatic) process and dictating one-sided demands is over".
A foreign ministry spokesperson said on Sunday that Tehran had clarified its broad positions via mediators to the US response but that additional points remained to be communicated to Washington.
"The Americans' propositions are more or less in line with their previous positions, specifically on the nuclear issue," spokesperson Esmaeil Baghaei said.
"We told them our focus in this stage is the issue of the Strait of Hormuz and the return to security in this waterway requires clear steps from the US."
Baghaei also denied Tehran had offered UN nuclear watchdog inspections of its nuclear facilities in exchange for US sanctions relief, saying Iran had not entered into nuclear discussions with Washington.
The document being circulated outlines a seven-day period of trust-building aimed at returning the two sides to an enhanced version of the memorandum of understanding agreed in June, including concrete steps on Iran's nuclear program, an official briefed on the talks said last week.
The disagreement centres on the sequencing of the steps rather than the components of the plan, the official added.
Qatar has been shuttling messages between Washington and Tehran in an effort to end the conflict and reopen the Strait of Hormuz, the conduit for a fifth of the world's oil and liquefied natural gas before the war that began at the end of February with US and Israeli attacks.
The June memorandum of understanding led to a brief ceasefire and included provisions on the strait and Iran's nuclear program.
Separately, Foreign Minister Abbas Araqchi told foreign ambassadors and diplomats in Tehran on Sunday that Tehran hoped Washington would choose diplomacy but warned that Iran was prepared to respond if the US again chose military action.
On Thursday, sources told Reuters that Iran was preparing a broader and more forceful response if Washington resumed large-scale military attacks.
"If they again move towards military solutions, we are more prepared than before and will take whatever action is necessary to defend ourselves," Araqchi said on Sunday.
Army spokesperson Mohammad Akraminia told Fars news agency on Sunday Iran would upgrade the range of its missiles.
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