Gulf mediation is still the named path, not a finished deal. Iran’s Sobh-e No newspaper, described by Iran International as close to chief negotiator Mohammad Bagher Ghalibaf, said Saturday that Tehran is reviewing a U.S. proposal conveyed through Qatar that sets a roadmap and timetable. The paper said Iran still demands Washington meet commitments first—including sanctions relief and release of frozen funds—and that Tehran’s principal conditions are unchanged after New York talks produced no agreement.

Ghalibaf publicly hardened the waterway line Sunday: Hormuz stays closed until seven conditions based on an Islamabad memorandum are met, Gulf News reported. Foreign Minister Abbas Araghchi told ambassadors Iran remains “serious about finding diplomatic solutions” while ready for a stronger military reply. On the U.S. side, Trump’s easy/hard-way warning and the Vance-chaired Camp David huddle keep force options visible beside the Qatar channel.

Into that thin Sunday text, Sen. Chris Murphy arrived in Qatar—calling himself the first Democratic senator to visit the region since the war began—and said he would also go to Riyadh to assess damage to U.S. facilities and discuss ending the conflict with Qatari and Saudi officials. Yemen’s Sunday Sanaa strikes and Aramco scare leave little quiet space for mediators.

For American readers, Qatar is still the phone line, not the finish line. Watch any State/Qatar readout, published roadmap language, and whether Murphy’s Gulf swing produces on-record mediation details.

What we know:
A U.S. proposal via Qatar is under Iranian review per Tehran-linked reporting; Ghalibaf restated seven Hormuz conditions; Murphy began a Qatar–Saudi visit Sunday.
What we don’t:
The full text of the U.S. roadmap, whether Qatar has a fresh bridging formula, or any near-term ceasefire timetable.