President Donald Trump said Tuesday that the war with Iran would be “over with very soon," but did not offer any details.

“Iran will not have a nuclear weapon. And they're failing very badly, very badly. That'll be over with very soon. It'll be over with very, very soon,” Trump said.

“They will not have a nuclear weapon. And oil prices are going to be tumbling down, just like they were before I had to make that little excursion to the Islamic Republic of Iran,” Trump said.

Trump’s remarks come after he rejected a ceasefire proposal from Iran over the weekend, telling reporters “that deal would not be acceptable.”

“'I’m rejecting their deal. They want to make a deal where we open the Strait immediately because they're losing so badly,” Trump said.

“We're winning tremendously -- we have total control of the Hormuz Strait,” he said on Saturday.

-ABC News’ Nicholas Kerr and Michelle Stoddart

Qatar is continuing its role as a mediator between Iran and the U.S., Qatari Foreign Ministry spokesperson Dr. Majid bin Mohammed Al-Ansari said Tuesday.

"The State of Qatar continues its meetings and exchange of messages between the parties to build common ground that brings viewpoints closer and leads to a peaceful solution,” he said. “It affirms its continued role in mediation and support for efforts aimed at de-escalation and restoring full freedom of navigation through the Strait of Hormuz.”

The United Kingdom Maritime Trade Operations (UKMTO) Centre reported that a vessel was "struck by a suspected unknown projectile" on Monday evening in the Strait of Hormuz.

The attack caused a fire aboard the vessel, UKMTO said, which was extinguished with no casualties or environmental impact reported. The vessel, it added, was still underway.

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