Trump made the announcement in a social media post as the Pentagon intensified its bombings of Iran's military, deploying B-2 stealth bombers from the US to strike at hardened, underground Iranian missile facilities with 900kg bombs.
US strikes also pummelled Iran's naval headquarters, largely destroying it, Trump said.
Iran's military is retaliating with hundreds of missile and drone attacks, and the US confirmed the first three deaths of US service members killed in combat on Sunday.
Another five have been seriously wounded during the conflict, the US military's Central Command said.
Two US officials, speaking on condition of anonymity, told Reuters the US service members were killed on a base in Kuwait.
Trump sought to brace the public for more casualties as he acknowledged the deaths, the first in major operations since he returned to office last year.
"We have three, but we expect casualties, but in the end it's going to be a great deal for the world," Trump told NBC News.
Trump said the armed conflict with Iran could last four weeks.
From the outset, it was assumed that it would take about four weeks, Trump said in a telephone interview with the British newspaper Daily Mail on Sunday .
"It's a big country, it'll take four weeks - or less," the US president said.
Trump, who announced plans to completely destroy Iran's Navy, said the remaining Iranian warships would soon be sunk.
"They will soon be floating at the bottom of the sea," Trump said.
"Other than that, their Navy is doing very well!"
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