The Persian Gulf Strait Authority (PGSA), a government body created by Iran during the ceasefire to manage crossings in the Strait of Hormuz, said in a statement on Monday that passage through the Strait is currently unfeasible.

They had been urging ships to visit their website to get a permit for passage.

"Due to recent hostile actions by the U.S. forces, passage through the Strait of Hormuz is currently unfeasible," the statement said. "As soon as stability and calm are restored, all applications will be reviewed in accordance with the scheduled timeline, and the permitting process will resume."

Trump said the U.S. will have Iran “under control very quickly,” touting the naval blockade in the Strait of Hormuz that is to resume on Tuesday.

"Well, I think it's going very fast. We've demolished their military. We're hitting them very hard,” Trump said when asked how long he expects the resumed war with Iran to last.

“We had a deal yesterday or the day before yesterday. It was all done, and then they broke up that deal immediately because they found out there was something in the deal they didn't like,” Trump said. “And they're wired differently, and we're not going to put up with it. We are just going forward. We're attacking them tonight. We're taking on all of their capability for anything having to do with the strait, with the Hormuz Strait. And I think in the end we will end up controlling the whole thing," Trump continued.

"But we'll have it -- we'll have it under control very quickly," Trump added.

As the U.S. continued strikes against Iran on Monday, Trump said, “The blockade was probably more effective even than hitting them, but I think the combination is the thing that, that really does it.”

-ABC News’ Michelle Stoddart and Emily Chang

U.S. Central Command said on Monday that a third consecutive night of airstrikes against Iran has begun.

It comes after President Donald Trump said in an interview with Hugh Hewitt that there would be more airstrikes against Iran Monday and Tuesday night.

During the interview, Trump railed against Iran, saying that the memorandum of understanding, which has fallen apart, was a test that failed.

"You know, it's a standard tactic in the U.S. that you go to a memorandum of understanding and then you go to the deal. I said, ‘Just go to the deal first.' But you know what? It was sort of a test, and they weren't there. They didn't honor the test," Trump said.

The White House has formalized its reengagement in the war in Iran, notifying Congress on July 10 of renewed military action, according to a copy of the notice obtained by ABC News.

The White House notes in the letter, addressed to Senate President Pro Tempore Charles Grassley, R-Iowa, that "United States ground forces are not involved in these strikes" and that they will be "limited, measured, planned, and executed in a manner designed to minimize civilian casualties."

ABC News has reached out to the White House for comment on the letter.

Many Democrats in Congress have argued that the administration exceeded its 60-day authority to conduct military operations against Iran without congressional approval under the War Powers Act. The White House has previously said that the ceasefire was put in place ahead of that 60-day limit and that it was never reached.

It's unclear how this letter might affect that timeline and whether Republicans will argue that the July 10 letter resets the clock.

-ABC News' Allison Pecorin