Trump's "Project Freedom" began Monday amid attacks in the Strait of Hormuz.
President Donald Trump announced "major combat operations" against Iran on Feb. 28, with massive joint U.S.-Israeli strikes targeting military, government and infrastructure sites.
Following the announcement of a two-week ceasefire, initial U.S.-Iran talks in Pakistan in April failed to reach a peace deal.
Trump later announced the open-ended extension of the ceasefire and the continuation of a U.S. blockade until negotiations are concluded "one way or the other."
Defense Secretary Pete Hegseth and Gen. Dan Caine, chairman of the Joint Chiefs of Staff, are scheduled to hold a press conference at 8 a.m. ET on Tuesday, according to the Department of Defense.
South Korea's Defense Ministry on Tuesday said it is "communicating closely with the United States and other relevant countries" regarding the situation in the Strait of Hormuz, after a South Korean-owned tanker was hit by an alleged Iranian attack off the coast of the United Arab Emirates on Monday.
President Donald Trump blamed Tehran for the incident, writing on social media of his "Project Freedom" operation that began Monday, "Perhaps it's time for South Korea to come and join the mission!"
The South Korean Defense Ministry said Tuesday that it had been "actively participating in discussions on international cooperation to ensure safe passage through the Strait of Hormuz."
The statement added that the ministry will "carefully review our position while comprehensively taking into account international law, the safety of international maritime routes, the [Republic of Korea]-U.S. alliance and the security situation on the Korean Peninsula and domestic legal procedures."
-ABC News' Joohee Cho and Joe Simonetti
Mohammad Bagher Ghalibaf, the speaker of the Iranian parliament who led Tehran's negotiating delegation to Islamabad in April, said in a post to X on Tuesday that Iran knows "full well that the continuation of the status quo is intolerable for America; while we have not even begun yet."
"The new equation of the Strait of Hormuz is in the process of being solidified," Ghalibaf wrote on X, in a reference to Tehran's claimed control of the strait. "The security of shipping and energy transit has been jeopardized by the United States and its allies through the violation of the ceasefire and the imposition of a blockade; of course, their evil will diminish."
U.S. Central Command began its "Project Freedom" mission on Monday to guide commercial shipping through the Strait of Hormuz despite continued Iranian threats against and attacks on cargo vessels in the strategic waterway.
Top Iranian officials have warned that the operation could prompt a new round of fighting, and on Monday the United Arab Emirates accused Iran of launching new missile and drone attacks against it.
During a phone interview with Hugh Hewitt on Monday afternoon, President Donald Trump refused to say whether the ceasefire with Iran was over after Iran fired at the United Arab Emirates and projected that the war could continue for another two or three weeks.
"Well, I can't tell you that," Trump said when pressed on whether the ceasefire is over. When asked if Monday's hostilities meant the beginning of a renewed conflict with Iran, Trump said that "one way or the other, we win."
"We either make the right deal or we win very easily. From the military standpoint, we've already won that. You know, you've heard me say it a million times, and other people say it. They had 159 ships. Hugh, now they have none. They're all at the bottom of the sea," Trump said.
The president stopped short of confirming whether Iran violated the ceasefire, saying "we'll see what happens" and instead touting the U.S. military capabilities.
Trump said the conflict could continue for "probably another two weeks" or "maybe three weeks," and emphasized that he is not operating under any time constraints. "Time is not of the essence for us," Trump said, while claiming significant public support for the war.
The president said the U.S. has "control" over the Strait of Hormuz amid the launch of the "Project Freedom" operation. "They said they were going to take over the Homruz Strait, and then we thought they might have. We took it over from them," Trump said of Iran.
On concerns over spiking oil prices, Trump said he thought prices might rise higher than they have -- perhaps as high as $250 -- claiming that the "genius" thing happening was ships were now heading to the U.S. for oil.
Asked about the future of Iran's enriched uranium stockpile -- Tehran's surrendering of which has been a key sticking point for the U.S. -- Trump downplayed its importance.
"From a standpoint of value, it's not very valuable. Probably can't be used. They may not be able to get it," Trump said, before touting the June military operation -- Operation Midnight Hammer -- to destroy Iran's nuclear capabilities. "I'd like to get it back so that they can't be tempted," Trump said of the enriched uranium.
Trump also said he is "convinced" that if the Iranian people had sufficient weapons, they would "fight back" against the regime.
-ABC News' Nicholas Kerr, Emily Chang and Michelle Stoddart
