Indirect U.S.–Iran diplomacy carried into Thursday after Iranian officials said they had received American feedback on Tehran’s seven-day trust-building plan through Qatari mediators. The Jerusalem Post, Asharq Al-Awsat, Al Jazeera’s live desk, and PBS Newshour’s prior mediation frame all describe Doha still shuttling ideas even after President Donald Trump publicly rejected Tehran’s earlier package and denied broad sanctions-relief reports.

Iran’s proposal centers on ending the U.S. port blockade, sanctions steps, and frozen-asset moves tied to reopening the Strait of Hormuz; Washington continues to demand nuclear concessions first. Iranian Foreign Minister Abbas Araghchi has been meeting Qatari intermediaries while cabinet officials review the U.S. reply. Trump has said the conflict could end “very soon” without publishing a full public text, and Defense Secretary Pete Hegseth’s battlefield claims about Iranian navy, air, and nuclear capacity remain contested — attribute those claims to the Pentagon, not as independent battle-damage assessment.

Oil and shipping desks still treat Hormuz as the chokepoint risk: Brent and product markets swing on mediation headlines and any kinetic scare. Sequencing is unchanged from midweek — nuclear traction before broad relief on the U.S. side; blockade and sanctions relief before a full reopen on Iran’s. Watch Qatar’s next relay, any formal published U.S. text, Araghchi’s travel, and whether strike rhetoric hardens. Overnight treats “reply received / under review” as the confirmed diplomatic beat, not a signed ceasefire.

As of Thursday, October 1, the public record on “Iran reviews U.S. Hormuz reply as Qatar mediation continues” still matches the facts above. Thursday’s lead coverage keeps the densest national and global wires in one place for morning readers. Reporting from The Jerusalem Post, Asharq Al-Awsat, Washington Examiner, New York Post anchors the Sources list; this card does not invent tallies, quotes, or outcomes beyond what those links support.