Iran live updates: Saudi Arabia says 2 of its airports were damaged in overnight strikes

In a Tuesday press conference, Islamic Revolutionary Guard Corps spokesperson Gen. Hossein Mohebbi said the U.S. should admit defeat in its war with Iran and "leave the region."

President Donald Trump had told "big lies," Mohebbi alleged, as he called for the American administration to "be changed."

"The enemy knows that Iran is not after nuclear weapons," Mohebbi said, referring to the U.S. "Their issue with Iran is not its nuclear programme but rather its vastness, which they want to destroy."

Mohebbi also dismissed U.S. assertions that the volume of shipping through the Strait of Hormuz -- the strategic waterway off Iran's south coast which has become the focus of the conflict -- was being restored.

"The fact that the Americans might manage, at great expense, considerable trouble and high risk to sneak a small vessel through the Strait of Hormuz under cover of darkness to export, say, 100 or 200 barrels of oil does not mean the Strait is open," Mohebbi said.

-ABC News' Victoria Beaule

In comments published by Iranian state media on Tuesday, Iranian Foreign Minister Abbas Araghchi discussed his meeting with Qatari mediators in New York following the United Nations General Assembly's high-level gathering last week.

"They had some ideas, and we agreed that they would raise the matter again with the American side, after which the U.S. side's final response would be conveyed to us," Araghchi said in a Monday briefing, as quoted by the state-run Islamic Republic News Agency.

Araghchi said Tehran submitted a seven-point proposal to the U.S. via Qatari mediators.

"Despite the comments made by the U.S. president, as I said, we are waiting for an official response from the United States through the mediators," Araghchi added.

-ABC News' Victoria Beaule

President Donald Trump is rejecting reports that say he is open to offering Iran sanctions relief and releasing its frozen assets in exchange for progress toward a nuclear deal, posting on Monday that he's offered Iran "NOTHING."

Trump specifically responded to an Axios report about possible economic relief for Iran if they present concrete nuclear concessions, writing in a post on his social media platform that the story is “untrue,” and that they should "withdraw this fake story, IMMEDIATELY!"

-ABC News' Isabella Murray

When asked about the progress of Monday’s mediated talks between the U.S. and Iran, President Donald Trump said, "We're going to win this as far as I'm concerned. It's going to be one way or the other. It's going to be -- it's going to go pretty quickly, too."

Trump continued to promise gas prices would come down after the war with Iran ends.

"We have the best economic numbers we have. Iran will never have a nuclear weapon. We're going to win that war very, very soon. It'll be over. And the gas prices will come tumbling down," Trump said.

-ABC News’ Isabella Murray and Michelle Stoddart