Iran live updates: Trump posts map labeling Strait of Hormuz 'new' US territory

Asked at an Oval Office event whether he's run out of “patience” with Oman, President Donald Trump responded, “I don't think they've behaved very well, but we'd handle them very easily, just like we do others."

Trump said again on Monday that U.S. control of the Strait of Hormuz -- a pitch he floated last week -- is a "great idea," while continuing to insist that Iran's military is "totally defeated."

Trump also claimed that the U.S. controls the Strait already.

“We control it with the blockade. And, I like the idea of declaring it a territory," Trump said.

Asked whether he was seeking an extension on the 60-day memorandum of understanding the U.S. signed with Iran on June 17-- an agreement now expiring -- Trump shook his head and mouthed “no.”

Asked whether he’s any closer to reaching a deal with Iran that would end their nuclear program, Trump said the Iranians "want to make a deal, but they're not going to make the kind of a deal that I feel is necessary."

-ABC News’ Michelle Stoddart

A reporter asked President Donald Trump on Monday if there was enough food aboard the USS Abraham Lincoln, a Navy aircraft carrier deployed to the Middle East, after reports surfaced suggesting the families of the servicemembers have raised concerns.

Trump responded there is enough food and blasted the reports as "fake news."

Trump also claimed that the Lincoln, which is marking a near-record-setting modern deployment as it has been out for over 260 days, hasn’t been out as long as ships have been in the past.

“The Lincoln has been out there for a period of time, good period of time. But over the years we've had them out there much longer,” Trump began.

“I was at a group meeting and an admiral came up to see me over the weekend, and it was at a big group, and he happened to be an admiral, retired. He said, 'I've been on ships. They're out there much longer than that, sir.' And I know people on the Lincoln. They say it's beautifully maintained and beautifully taken care of,” he said.

On Friday, Trump said the Lincoln hasn't been deployed for "nearly long enough."

Democrats are demanding an investigation into the conditions aboard the Lincoln after reports of low morale among sailors during the extended mission.

-ABC News’ Michelle Stoddart

Speaker of the House Mike Johnson said he believes the U.S. is “in the process” of “resolving” the Iran war.

“The Iran conflict has been the cause, of course, of gas prices going up. It’s drug on,” Johnson said during a campaign visit in Virginia.

“I believe ultimately that we'll be, there'll be a coalition of nations, a combination of allied NATO allies and Arab states in the region. Everybody in the world has an interest in the Strait of Hormuz being open for commerce, and so I believe we'll be getting into a new phase of that, where we can calm this down,” Johnson said.

“That will hold gas prices down to planet Earth, and that will also bring down grocery prices,” he said.

-ABC News’ Lauren Peller

The Iran-aligned Houthi rebels in Yemen said on Monday they launched a series of new attacks against the Saudi-backed, internationally recognized government forces of Yemen.

Houthi military spokesperson Yahya Saree said in statements posted to Telegram that Houthi forces struck several Saudi military boats off the coast of the Red Sea port of Mocha, which is held by the Saudi-backed Yemeni forces.

Saree said the group used ballistic missiles to target, "a military landing craft belonging to Saudi enemy forces -- along with four accompanying gunboats."

Saree later said that the Houthis had also targeted an arms depot in the Marib region, east of the capital Sanaa, using drones.

-ABC News' Victoria Beaule