The head of Iran's Supreme National Security Council, Mohsen Rezaei, told al-Jazeera in an interview that Iran is waiting for US President Donald Trump's response after Iran passed on a message via Qatar.
It was not clear when the conditions were shared.
Rezaei said they include ending the war on all fronts, releasing assets seized from Iran and ending the US naval blockade of Iranian ports.
He added that consultations were continuing with Qatari and Pakistani mediators
Earlier US-Iran negotiations fell apart.
In mid-June, the US and Iran signed a 14-point framework agreement intended to pave the way for a final agreement on a permanent end to the war.
The parties undertook to negotiate a final agreement within an initial period of 60 days.
An extension was to be possible by mutual agreement but this did not happen.
The agreement also stipulated that Iran should do its utmost to ensure the safe and toll-free passage of merchant ships through the Strait of Hormuz for 60 days.
This clause in particular sparked a new dispute between the US government and the Iranian leadership.
In return, the US was to end the naval blockade of Iranian ships and ports.
The US agreed to unfreeze Iranian assets, with the specific procedures and amounts to be determined during the subsequent negotiations.
Rezaei also said on Saturday that Iran wants the fighting between Saudi Arabia and the Houthi militia in Yemen to end, adding that he believed Yemenis also wanted a settlement with Saudi Arabia.
Meanwhile, the head of United States Central Command said the military has supported the transit of a billion barrels of oil through the Strait of Hormuz over the past two months and insisted that Iran had "exported zero barrels" because of the US blockade.
Admiral Brad Cooper said the strait's primary transit lanes have been cleared of mines, and the volume of oil, natural gas and cargo transiting over the past two weeks is the highest it has been in six months - or shortly after the war began with US and Israeli strikes.
But monitors say shipping traffic remains well below pre-war levels.
Iranian forces continue to attack ships as they assert control over the waterway through which about one-fifth of the world's traded oil and natural gas passed before the war.
with AP and DPA
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