Sgt. Benjamin N. Pennington, 26, was killed in Saudi Arabia.
President Donald Trump announced "major combat operations" against Iran on Feb. 28, with massive joint U.S.-Israel strikes attack targeting military and government sites, officials said.
Iranian state television confirmed that Ayatollah Ali Khamenei was among those killed in Tehran on the first day of strikes. His son Mojtaba Khamenei was chosen on Sunday to succeed him.
Iran is responding to the operation with missile and drone attacks targeting Israel, regional U.S. bases and multiple Gulf nations. Israel is also intensifying its long-running strike campaign against the Iran-backed Hezbollah militia in Lebanon.
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The Kuwaiti Air Defense Force has intercepted "a number of hostile aerial targets" on Monday, a spokesperson for the ministry said in a statement.
The missiles targeted the central part of the country, with no casualties recorded, the statement said.
The Israel Defense Forces said it has launched strikes targeting Hezbollah in various parts of Lebanon.
The announcement comes after the IDF had said earlier on Monday that Lebanon had launched projectiles toward northern Israel that were intercepted.
Reza Pahlavi, the exiled former crown prince of Iran, said in an interview with "60 Minutes" on Sunday that he wants to be a "transitional leader" in Iran -- not "the future king or future president."
"They trust me as a transitional leader, not as the future king or future president or future whatever. I'm totally focused on my mission in life, which is let me bring the country to a point that they can make that free choice. That would be enough for me having said mission accomplished," Pahlavi said.
He said that he imagines a future where Iran is at peace with Israel, saying, "The strategic importance of having a partnership with Israel is critical."
Pahlavi also said that the nation's nuclear program should be "totally dismantled."
Pahlavi's father, Mohammad Reza Pahlavi, was the last shah of Iran. In 1979, he left Iran amid rising political tension. Ayatollah Khomeini came to power in 1979, following the success of the Iranian Revolution.
President Donald Trump returned to the White House on Sunday night from Mar-a-Lago, but he did not take questions from reporters about the operation in Iran or the recent U.S. casualties.
The president instead went to the Rose Garden to inspect newly installed statues of the Founding Fathers.
"Unbelievable statues. You'll see. Come and look at them," he told reporters.
