Special Envoy Steve Witkoff said that the U.S. and Iran engaged in indirect talks through “mediators” at the United Nations General Assembly in New York on Tuesday.

“Today, on the sidelines of the United Nations General Assembly, we engaged in lengthy talks with the Iranian delegation through the mediators, who shuttled between the two sides throughout the day,” Witkoff said in a post on social media Tuesday night.

Witkoff said that the unspecified mediators “successfully completed a round of discussions” and that their work will continue.

It’s unclear exactly who is mediating on behalf of the U.S. and who from the Iranian delegation participated.

Witkoff's readout comes after President Donald Trump told reporters on Tuesday that his aides met with the Iranian delegation -- though he declined to specify who. Later in the afternoon, Trump noted the meeting was actually with mediators.

Earlier in the day, Trump had represented to reporters that his aides had directly met with the Iranian delegation, replying “yes” when asked whether anyone from his team had met with them, and describing it as a three-hour meeting.

-ABC News' Nicholas Kerr

Trump said he thinks there’s a "lot of momentum" for Iran and the U.S. to make a deal right now, following the talks his team had with the Iranian delegation Tuesday, but also repeated his past claims that the conflict wouldn’t end until after the midterm elections.

"We've been mediating for a while, but I think there's a lot of momentum for them to make a deal," Trump said during the meeting of the Gulf Cooperation Council on Tuesday.

Trump later touted Operation Economic Outcast, his administration’s sanctions program against Iran, saying it’s putting pressure on Iran to negotiate before "it's too late" for it to "survive as a nation."

The president later said he was unclear on when the war would end.

"We think that the situation with Iran could end right after the midterm elections, and maybe before. I don't know. You never know," he said.

Trump said his efforts to end the war, or even his starting the conflict, had nothing to do with the upcoming elections.

The president later went on to reiterate his threats against Iran, claiming they can either agree to make a deal or "it's going to end very very quickly."

-ABC News' Fritz Farrow and Isabella Murray

President Donald Trump said his team had a three hour meeting with the Iranian delegation at the U.N. General Assembly on Tuesday, and said Iran faces "potential greatness or obliteration."

Trump's comment came and after he threatened to "annihilate" Iran during his speech to the assembly earlier in the day.

The president told reporters during a bilat with Ukrainian President Volodymyr Zelenskyy, that it was a "very good meeting," and said he couldn't imagine why Iran wouldn't want to make a deal.

"It's a greatness, potential greatness or obliteration. In one case, it's obliteration. And the other alternative is potential greatness. It can be a great country," he said.

Trump later  confirmed that Special Envoy Steve Witkoff or Jared Kushner were the members of his team who met with the Iranians. 

"I can tell you that Steve and Jared met with the mediators on Iran deal. The mediators were here, not the highest level, but did something. A lot of good thoughts. A lot of things are working out very well," Trump said during  the "Shield of the Americas" anti-cartel coalition meeting on the sidelines of U.N. General Assembly. 

-ABC News' Isabella Murray, Fritz Farrow, Michelle Stoddart and Nicholas Kerr

Iran's Foreign Minister Seyed Abbas Araghchi took a few meetings with foreign dignitaries, Iranian officials said.

He met with the Italian Foreign Minister Ignazio Cassis, Kaja Kallas, the European Union’s High Representative for Foreign Affairs and Security Policy, and held talks with Qatar’s Prime Minister and Foreign Minister Mohammad bin Abdulrahman Al Thani, according to Iranian officials.

-ABC News' Desiree Adib

In an interview with NBC's "Today" on Tuesday morning, Secretary of State Marco Rubio said that President Donald Trump is "open" to meeting with his Iranian counterpart, Masoud Pezeshkian, at this week's United Nations General Assembly meeting in New York.

Trump, Rubio said, "has said he's open to meeting with anybody. This is a president that will meet with anybody, for the most part, because he believes that engaging with people is important if you're going to solve problems."

"I don't think anything is scheduled at this point, but we're certainly open to something like that," Rubio added.

Asked about rising prices associated with the ongoing war, Rubio replied, "Anyone who is concerned about prices itself is not wrong, and obviously if the war is being blamed for that, then of course you're going to hear it." He added, "We recognize that. We don't want prices to be high."

Rubio asserted that if Iran obtained a nuclear weapon, the price of a gallon of gas would be "double."

"Because then no one would touch them. There's nothing you could do about Iran and they would use that nuclear weapon to control the Straits of Hormuz forever. They would be able to choke off the world's energy supply any time they wanted," he said.

Rubio said roughly 60% to 70% of the oil flows through the Strait of Hormuz had been restored, but pointed to Houthi attacks on Saudi oil infrastructure as a reason prices remain high.

-ABC News' Shannon K. Kingston