According to Trump, the US goal is to destroy the mountain Kuh-e Kolang Gaz La, also known as Pickaxe Mountain, which is located near the Iranian nuclear energy facility in Natanz.
He claims that despite the attacks, a peace agreement is still possible.
"We had a deal with them two days ago, but then they said they couldn't agree to it and needed to negotiate more," Trump told reporters in the Oval Office shortly after the new wave of attacks began at 11 p.m., Swedish time.
Trump had then warned of "powerful" attacks on Iran.
The aim, according to a statement from the military command center Centcom, is to inflict significant damage on "Iranian forces and impair their ability to attack innocent civilian and commercial vessels in the Strait of Hormuz."
Earlier on Monday evening, Iranian state-controlled media reported new explosions on Iranian soil, including outside the large port city of Bandar Abbas and on the island of Larak.
