Iran's Foreign Minister Abbas Araqchi and US envoys Steve Witkoff and Jared Kushner communicated through mediators on the sidelines of the UN General Assembly in New York, the first such contacts since an interim ceasefire agreement collapsed in July.
"Steve and Jared had a very productive meeting today with mediators of Iran, merely mediators. Let's see what happens with that," US President Donald Trump said on Tuesday.
"They've been mediated for a while, but I think there's a lot of momentum for them to make a deal. It's what we're hearing from everybody."
Earlier, Trump had told the UN General Assembly in a speech that he had to decide whether to make a deal with Iran or "annihilate" the country.
Iran's President Masoud Pezeshkian was due to address the gathering on Wednesday.
Iranian foreign ministry spokesman Esmail Baghaei said Tehran had engaged with the United States through a Qatari mediator in New York and conveyed conditions, including an end to the war on all fronts and a halt to US "acts of aggression".
Some Iranian state media had earlier reported that Araqchi and Witkoff had met, but Iranian officials clarified to Reuters that this was not face-to-face.
Araqchi met the prime minister of Qatar, Sheikh Mohammed bin Abdulrahman Al Thani, who has been one of the main mediators at previous talks.
The diplomatic opening helped keep oil prices near two-week lows, with Brent crude now holding just below the $US100-a-barrel threshold it had shot through in September after Houthi fighters in Yemen launched a major offensive and fired into Saudi Arabia.
The war, launched by Trump in February alongside Israel as "Operation Epic Fury", has lasted nearly seven months, killing thousands of people, disrupting global energy supplies and spreading to other countries in the region - first to Lebanon and more recently to Yemen.
Trump repeated previous assertions that the war could end around the time of November's US midterm elections, though he has not explained why.
Since diplomacy broke off in July, the sides have repeatedly exchanged fire, although Trump has held back from a full-blown resumption of strikes after receiving advice from his military commanders that munitions were running low.
An interim agreement reached in June and signed by Trump and Pezeshkian would have given Iran its main demands: lifting financial sanctions and unfreezing assets in return for talks on limiting its nuclear program.
But that deal unravelled within weeks over shipping rules in the Strait of Hormuz, conduit for a fifth of global oil and liquefied natural gas before the war.
Iran wants to exert greater control of the strait and collect fees from ships that use it, which Washington rejects.
Despite near-daily attacks on tankers, traffic through the strait has gradually increased in recent weeks, as oil producers pay shipping companies to switch off transponders, navigate the route and transfer crude to other vessels beyond the strait.
Exports from the United Arab Emirates have already recovered to pre-war levels, and Saudi Arabia has sold 60 million barrels of Gulf oil for September and October, to be delivered beyond the strait off the coast of Oman, a big increase from August.
Even so, disruption continues to squeeze global energy markets and fuel inflation.
The risk of further disruption has increased since the Iran-backed Houthis advanced in Yemen this month, threatening traffic through the Bab el-Mandeb Strait at the southern entrance to the Red Sea, an alternative export route used by Saudi Arabia.
Washington, for its part, has imposed a blockade on Iranian ports, deepening Iran's economic crisis.
