Confirmation of a structured, mediator-led process, rather than one-off contacts, chips further at the geopolitical risk premium in crude, adding to pressure from recovering Saudi exports and rising Hormuz traffic. The indirect format and Iran's long list of conditions suggest a deal remains distant, so downside is likely to be gradual and headline-driven rather than a one-way slide. Any sign that talks are stalling, or fresh Houthi attacks on Saudi infrastructure, could quickly rebuild the premium. Refined products, with diesel already at record highs, remain the tightest part of the market and may respond less to diplomatic progress than crude.---Washington and Tehran are now talking in earnest through intermediaries in New York, enough to take a little more heat out of oil, if not yet enough to settle the war.Summary:US special envoy Steve Witkoff said US and Iranian delegations held lengthy indirect talks on the sidelines of the UN General Assembly, with mediators moving between the two sides throughout the dayHe said a round of discussions had been completed that Washington hopes will prove constructive and promising, and that mediators will continue their workTrump separately said US officials met an Iranian delegation for about three hours in a productive meeting, with another planned, but also said a peace deal would come after November's US midterm electionsIran has set out conditions for talks, including an end to the war on all fronts, release of frozen funds, lifting of the naval blockade and sanctions, and an oil waiverQatar and Pakistan have reportedly entered mediation, and Iranian President Masoud Pezeshkian arrived in New York on TuesdayOil prices eased, extending Tuesday's losses driven by Saudi Arabia's East-West pipeline restart and rising flows through the Strait of HormuzThe United States and Iran held lengthy indirect talks on the sidelines of the UN General Assembly in New York, US special envoy Steve Witkoff said, as diplomatic efforts to end the war gathered pace and oil prices edged lower.In a post on X on Tuesday, Witkoff said mediators had shuttled between the US and Iranian delegations throughout the day and that the two sides had completed a round of discussions that Washington hopes will prove constructive and promising. He said the mediators would continue their work, but gave no details on the substance of the talks or a timeline for further rounds.The update adds to signals from US President Donald Trump, who said earlier on Tuesday that US officials had met an Iranian delegation for about three hours in a meeting he described as productive, with another expected soon. Trump has said he believes a settlement will be reached, but he also said a peace deal would come after the US midterm elections in early November and warned that the US could destroy Iran without an agreement. Trump has also said he would be open to meeting Iranian President Masoud Pezeshkian, who arrived in New York on Tuesday for the General Assembly.Tehran has set a high bar for any agreement. According to reports, Iran's conditions for resuming talks include an end to the war on all fronts, negotiations on a timeline for a full Israeli withdrawal from southern Lebanon, the release of frozen funds, the lifting of the US naval blockade and newly imposed sanctions, an end to military threats and an oil waiver. Iranian media earlier pushed back on a report that Iran could reopen the Strait of Hormuz within seven days if the US eased military pressure and lifted its blockade.The mediation effort has broadened in recent days. Qatar and Pakistan have reportedly stepped in between the two sides, and Iran has reportedly asked China to take a greater role in bringing Washington and Tehran to the table.Oil prices eased on the diplomatic progress, extending a decline driven by improving supply. Brent settled around $99 a barrel on Tuesday and WTI near $95, after Saudi Arabia restarted its East-West pipeline and prepared to resume exports from the Red Sea port of Yanbu. Saudi crude flows through the Strait of Hormuz have also recovered sharply in recent weeks. The pipeline had been shut since mid-September after drone attacks, and Yemen's Houthis have continued to claim strikes on Saudi targets, a reminder that supply risks have not gone away.Analysts expect prices to remain sensitive to headlines. One said crude was likely to stay range-bound until there was either clear progress or a setback in US-Iran diplomacy. The next test will be whether mediators can narrow the gap between Washington's timetable and Tehran's conditions, and whether a second round of talks follows quickly. This article was written by Eamonn Sheridan at investinglive.com.