Iran live updates: US, Iran passing messages through intermediaries, Tehran says

Messages between the United States and Iran were being passed "through intermediaries," an Iranian official told state media on Sunday, adding that that "the process should not be called negotiations."

Foreign Minister Abbas Araghchi alleged that the United States continued to violate June's memorandum of understanding, reportedly saying that until that "comes to an end and the United States compensates for what it has violated, the possibility of resuming negotiations does not exist."

Araghchi also reiterated, according to state media, that an agreement with Oman does not mean the Strait of Hormuz will be reopened.

An opening "of the Strait of Hormuz is contingent on the fulfillment of other conditions, and these conditions have been conveyed to the American side through intermediaries," he reportedly said.

-ABC News' Rashid Haddou

The Strait of Hormuz will never fully reopen until the United States "corrects its behavior," Mohammad Bagher Zolghadr, secretary of Iran’s Supreme National Security Council, said in a statement Saturday.

Zolghadr said the U.S. must stop making threats or insults against Iran, end military action against Iran and its regional allies, withdraw its naval and air forces involved in a blockade against Iran, compensate Iran for damage caused during the recent conflict, lift sanctions, and release frozen Iranian assets.

U.S. negotiations with Iran have progressed this week, Vice President JD Vance said on Saturday, but he stressed that the conflict is not over.

"I try to remind people we're really in the middle of the game here. This thing is not over. It’s obviously not at the beginning, we’re in the middle of the game. And we’re applying a whole host of tools, diplomatic, economic, military tools to ensure that we get the best outcome for the American people,” Vance said during an interview on Fox News.

"They're hurting in a big way. They want this thing to be over. The question is whether they're able, their system is able, to give the things that are necessary for us to be happy, for us to feel like we've gotten what we need out of this particular engagement. That is still to be determined," he said.

Vance said the current negotiations are focused on conditions for the U.S. to "maximize oil and gas" coming out of the Strait of Hormuz so that "Americans can enjoy lower gas and energy prices."

Pressed on the fact that Iranians have said they’re looking to tighten their grip on the strait amid the negotiations, Vance rejected that premise, saying there are active talks going on -- including other Gulf states -- about how to allow for safe flow of traffic through the Strait.

Oman's foreign ministry stressed the importance of avoiding actions that could impact "ongoing" negotiations with Iran regarding the navigation through the Strait of Hormuz in a statement Saturday.

Oman condemned the "repeated attacks" of ships passing through the strait. The statement did not mention Iran directly, but urged against acts "that could affect these negotiations and the progress achieved, which takes into account the interests of all parties."

Oman said negotiations were "proceeding in a positive and constructive atmosphere."

This comes after the United Arab Emirates blamed Iran for targeting a ship used by the Abu Dhabi National Oil Company.