Following a meeting with Israeli Prime Minister Benjamin Netanyahu on Monday, President Donald Trump's son-in-law and special envoy Jared Kushner told Fox News of what he called a "very, very" good meeting about the Trump administration's Gaza peace plan.

The meeting came amid deep skepticism from Netanyahu about the next steps in pursuing peace with Hamas. Kushner separately met with Hamas officials over the weekend.

"I think there were some valid concerns that they raised that we were able to address, and we were able to go through some of the misunderstandings and misinformation that's been out, as well," Kushner said of his meeting with Netanyahu.

Kushner said he urged Netanyahu to give Hamas the chance to prove themselves -- "and if they don't follow through now on their commitment, everyone will see that they're not genuine about peace and that Israel will have a lot more support from the U.S. and others to go on and finish the job in an appropriate way."

Kushner insisted that Hamas will need to hand over its weapons and suggested the group could do so in as little as 30 days. He said tunnels built by Hamas could be filled up within the next 60 to 90 days.

"We're very committed to the fact that we have the plan to rebuild Gaza, but we will not allow Gaza to be rebuilt until the demilitarization occurs. Nobody wants to put more money into a place that's gone on for so long, if it's just going to be taken over by terrorists or blown up again," Kushner said.

On his meeting with Hamas leaders, Kushner said "they said all the right things," but the U.S. remains skeptical until they see real action on the ground.

"It's very, very hard to trust a terrorist organization that committed these terrible atrocities. We had a very cordial meeting, and they said all the right things. We're going to give them a chance to perform, and it's going to be based on actions and steps. And I hope it will be true," Kushner said.

-ABC News' Mariam Khan

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