In a private gathering on the sidelines of the UN meeting, Tehran described its new proposal to the US. The conditions for Washington largely echo the ones agreed to in the June deal that fell apart.
The strait is crucial for the world's oil supply and central to the conflict between the US and Iran, which remains deadlocked after nearly seven months.
Under the plan, Iran would reopen the Strait of Hormuz by the end of the seventh day if certain conditions were met, following which nuclear talks would resume.
Tehran is seeking to maintain a stranglehold on the vital waterway in its war with the United States, while Washington has kept up a counterblockade of Iranian ports.