US President Donald Trump said that talks with Iran regarding its nuclear program are going well.

"I think it's going well. Nothing matters until they're over, so I don't like to talk about it. But it's going well. I think things with Iran are going very well," he told reporters aboard Air Force One.

Iran said earlier that the United States wants a nuclear agreement "as soon as possible," after rare talks in Oman on Saturday, while Trump threatened military action if efforts to reach a new deal fail.

The Iranian side was led by Foreign Minister Abbas Araqchi, a seasoned diplomat and one of the architects of the 2015 Iran nuclear deal, while US President Donald Trump's envoy, real estate mogul Steve Witkoff, led the US delegation. The two men met briefly face-to-face.

Araghchi told Iranian state television that the US side indicated it wanted to reach an agreement "as soon as possible, but that it would not be easy and would require preparation from both sides."

"In today's meeting, I believe we have come very close to establishing the foundations for negotiations... Neither we nor the other party want fruitless negotiations, discussions for the sake of discussions, a waste of time, or endless negotiations," he continued, adding that a new meeting will be held "next Saturday" with the aim of reaching an agreement "as quickly as possible."

"Today's direct engagement with Special Envoy (Steve) Witkoff was a step forward in achieving a mutually beneficial outcome," the US presidency said in a statement, adding that the two sides agreed to "meet again next Saturday."

Iran reported that Omani Foreign Minister Badr al-Busaidi mediated the high-level talks in Muscat.

"Our position today," Witkoff told the Wall Street Journal, "is to demand that Iran completely dismantle its nuclear program, a position held by Trump's hardliners but one that few expect Iran to accept."

He added, "This does not mean that, on the sidelines, we will not find other ways to reach a settlement between the two countries," stressing that "the red line for us is not militarizing Iran's nuclear capability."