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

U.S. armed forces will resume their blockade of the Strait of Hormuz Tuesday, according to U.S. Central Command.

"At the Commander in Chief's direction, U.S. Central Command (CENTCOM) forces will resume blockading maritime traffic entering and exiting Iranian ports on July 14 at 4 p.m. ET," CENTCOM announced Monday afternoon.

"CENTCOM forces will enforce the blockade against vessels transiting to or from Iranian ports and coastal areas," the statement further said, adding that the U.S. military "continues to support traffic flow through regional waters for all vessels not violating the blockade."

President Donald Trump announced earlier Monday that the U.S. would reinstate the naval blockade against Iranian ships and ports and would charge a 20% fee on all cargo shipped through the Strait of Hormuz.

Iran pushed back swiftly against the president's declaration, with IRGC spokesman Ebrahim Zolfaqari saying in part that Iran "will under no circumstances allow the United States to interfere in the management of the Strait of Hormuz" and "will deal forcefully with any disruption to the passage of commercial vessels and oil tankers by the invading and pirate U.S. military."

Iranian Foreign Minister Abbas Araghchi said in response "POTUS is absolutely right. Whoever provides secure and safe passage of commercial vessels through the Strait of Hormuz should be compensated for this service. Iran has always been the GUARDIAN of the Strait and will remain so FOREVER. 20% is of course too much. We will be fair."

Oil prices climbed steadily all day amid the escalating rhetoric and are now spiking more than 9%. U.S. oil is now selling at around $78 a barrel and global oil is at about $83 a barrel.

-ABC News' Steven Beynon, William Gretsky and Zaki Zunaira