Trump's "Project Freedom" also began 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."
The United Arab Emirates said its air defense systems engaged with 12 ballistic missiles, three cruise missiles and four drones launched from Iran on Monday.
The attacks resulted in three moderate injuries, the country's Ministry of Defense said, adding that it "remains fully prepared and ready to deal with any threats and will firmly confront anything that aims to undermine the security of the country."
President Donald Trump stopped short of saying the U.S.-Iran ceasefire has been violated, following reports of Iranian attacks on commercial vessels near the Strait of Hormuz and on oil infrastructure in the United Arab Emirates.
"[It was] not heavy firing," Trump said in a phone call with ABC News chief Washington correspondent Jonathan Karl when asked if the ceasefire had been violated. "We'll let you know. Ships are moving. You know, we moved quite a few last night -- big ones. There was no firing. I guess there has been some recently. I'm looking into it."
Over the past several hours, Iran fired on a South Korean ship near the Strait of Hormuz and fired missiles and drones on the UAE. And, according to U.S. Central Command, U.S. forces fired on six Iranian fast boats and intercepted several Iranian missiles and drones.
Trump told ABC News that Iran "better hope [the ceasefire] remains in effect. The best thing that can happen to them is that we keep it in effect."
And what happens if the ceasefire is broken?
"I'll let you know, like I'll let everyone else know," he said. "We just heard about this, and we'll find out about it. What should happen is South Korea should get involved. It was a South Korean ship that got hit. And I would think, if you have a ship that's hit, you should immediately send some people."
Asked about the attacks on the UAE, Trump said the missiles and drones were "shot down for the most part."
"One got through. Not huge damage," he said.
On what this all means about the prospects for ending the war, Trump said, "We have it under control. One way or the other, we win. And you know why, Jon? I always win. You found that out a long time ago."
The U.S. took out six small Iranian boats that were "threatening commercial shipping" on Monday, Adm. Brad Cooper, the head of U.S. Central Command, told reporters during an update on "Project Freedom."
Cooper said that over the past 12 hours, the Islamic Revolutionary Guard Corps has been launching missiles, drones and small boats toward ships the U.S. was protecting in the Strait of Hormuz, and that the U.S. "defeated each and every one of those threats" through defensive munitions. AH-64 Apache attack helicopters and others were used to "eliminate" the boats, he said.
No U.S. military ships have been struck, Cooper said.
The United Arab Emirates' Ministry of Defense said it is "currently engaging" with air attacks from Iran, and that its air defense systems were intercepting ballistic missiles, cruise missiles, and drones.
This marks the first time the UAE, or any Gulf country, has come under significant attack by Iran since the ceasefire took hold in early April.
Multiple flights headed to the UAE are now diverting to Muscat, Oman, amid reports of drone and missile attacks, according to Flightradar24 data.
Amid the reports, the British military's United Kingdom Maritime Trade Operations center also said a cargo ship was on fire off the coast of the UAE. The cause of the fire was not yet confirmed.
