Iran live updates: US 'taking over' Strait of Hormuz, Trump says

President Donald Trump asserted Monday that the U.S. is "taking over" the Strait of Hormuz, asserting that he planned to run and protect the critical waterway and get paid for doing so.

"Well, we're taking over the Strait. They have nothing. They've got nothing," Trump said in a live phone interview with "Fox and Friends" following the latest exchange of strikes between the U.S. and Iran.

"We're going to keep the Strait and we'll probably run it. We'll become the guardian of the Strait. Maybe we'll call it the guardian angel of the Strait, and we should be reimbursed for that," Trump added.

The president did not say how the U.S. would be paid, though he's previously floated charging a toll on vessels transiting the strategic waterway.

Trump said the U.S. attacked Iran on Sunday night which he claimed was retribution for Iran reneging on its commitments under the memorandum of understanding signed by the combatants last month.

"We hit them very hard last night. Every time they send a drone, we hit them very hard. But we had a deal. But nobody knows we had a deal. It was a done deal. And then they broke it," the president said.

The president also claimed that there was an 11-hour meeting with Iranian representatives on Sunday and that Iran had agreed to "everything" before later proposing "changes." The president did not specify what changes Iran had proposed. Iranian representatives held talks in Oman on Saturday without U.S. diplomats present.

The White House did not immediately respond to a request for comment about the meeting.

-ABC News' Nicholas Kerr

U.S. oil was trading at $72.83 per barrel -- up about 2% -- as of Monday morning after the latest round of exchanges between U.S. and Iranian forces. Global oil was trading at $77.52 per barrel, also up around 2%.

The national average price for a gallon of regular gas was $3.81 on Monday, according to data from GasBuddy -- up 9 cents since last week.

Traffic through the Strait of Hormuz has slowed in recent days, according to latest data from global ship tracking firm Kpler. Fourteen ships crossed through the strategic waterway on July 12, compared with 24 ships on July 11.

-ABC News' Zunaira Zaki

Iranian Foreign Ministry spokesperson Esmaeil Baghaei said during a press conference on Monday that the memorandum of understanding between the U.S. and Iran "has entered a crisis stage," following the escalation in attacks over the past week.

Baghaei argued that any points of the agreement Iran did not fulfill were a direct result of the U.S. having "violated its commitments," as quoted in a write up published by the official Islamic Republic News Agency.

Addressing rumors that weekend talks in Oman addressed broader issues, including nuclear talks, Baghaei said that the discussions "were solely focused on the issue of the Strait of Hormuz."

"Our effort was to reach a mechanism in consultation with Oman that would ensure the safe passage of ships through the Strait of Hormuz," Baghaei added. No agreement was reached, he said, because of "overt and covert pressure from the U.S. on Oman."

Baghaei said Iran was adhering to the Strait of Hormuz clause in the memorandum of understanding and that Tehran has the right and obligation "to take the necessary measures to protect our security and national interests," adding that the Strait and surrounding areas had been "misused to harm Iran's security and national interests."

The presence of U.S. warships escorting commercial vessels through the Strait, Baghaei said, "confirms the U.S.' insistence on continuing insecurity in the region."

Baghaei also defended Iran's ongoing attacks on neighboring countries, claiming that Iran was only targeting "the bases, facilities, and positions used by the United States to attack Iran, including its logistical and support facilities."

Among the issues still to be addressed in any final peace settlement is the scale and nature of Iran's nuclear program. Baghaei on Monday dismissed the idea that Rafael Grossi -- the director of the International Atomic Energy Agency -- would be allowed to access Iran's nuclear facilities.

-ABC News' Victoria Beaule

Kuwait's Army Headquarters said in a post to X on Monday that the Gulf nation's air defenses were again "confronting hostile aerial targets within Kuwaiti airspace."

In Jordan, the military said it shot down four Iranian missiles, adding that there were no casualties or damage.

Bahrain's Interior Ministry, meanwhile, said in the early hours of Monday that the country's air defense sirens were activated, but Manama did not confirm any fresh attacks.

-ABC News' Will Gretsky and Victoria Beaule