In a potential new flashpoint, Iran also threatened to act against its neighbours if they abide by new US sanctions intended to ground Iranian civilian aircraft worldwide.
Washington has said it will impose so-called secondary sanctions against any country that allows Iranian flights after Wednesday. Mohsen Rezaei, secretary of Iran's Supreme National Security Council, told state TV Iran would ensure neighbouring countries' airports could not function if they stop Iranian flights.
The annual UN gathering in New York provided the occasion on Tuesday for Iranian and U.S. officials to hold their first known indirect talks since a ceasefire collapsed in July, with Iran's Foreign Minister Abbas Araqchi and US envoys Steve Witkoff and Jared Kushner communicating through mediators on the sidelines.
"Steve and Jared had a very productive meeting today with mediators of Iran," Trump said on Tuesday after his own speech. "I think there's a lot of momentum for them to make a deal. It's what we're hearing from everybody."
Iranian Foreign Ministry spokesperson Esmail Baghaei said Tehran had engaged with Washington through a Qatari mediator and conveyed conditions, including an end to the war on all fronts and a halt to US "acts of aggression".
Some Iranian state media initially reported that Araqchi and Witkoff had met, but Iranian officials clarified to Reuters that it was not face-to-face.
The diplomatic contact in New York caused a backlash in Iranian media associated with hardliners.
An opinion piece run by the semi-official Tasnim news agency, associated with the Revolutionary Guards, said Araqchi was wrong to have contacts with Witkoff and Kushner, "a major gift to Trump", as Iran had already conveyed its terms.
Iranian sources told Reuters the delegation had been ordered not to meet the Americans face-to-face by the Supreme National Security Council, a body that includes figures selected by Ayatollah Mojtaba Khamenei, the supreme leader. Khamenei has yet to appear in public since replacing his father, who was killed on the war's first day.
One Iranian journalist covering the visit told Reuters that some hardliners viewed the trip to New York itself as an insult to the memory of the slain leader, Ali Khamenei.