Trump wrote on social media he would hold Iran accountable for any further attacks by the fighters, "and major military punishment will be inflicted upon Iran and, of course, the Houthis, themselves".
He told Axios he was considering re-launching major combat operations in Iran and was close to a decision.
"They haven't received enough pain yet," the U.S. news outlet quoted Trump as saying.
Trump also said on social media that any damage to cargo ships would be paid for with Iranian money, referring to frozen Iranian assets held by the United States, but without specifying how.
Iranian Foreign Minister Abbas Araqchi responded with a warning on X, saying no one's assets were safe once governments normalised such confiscation. "Ensuing chaos will not be pretty or peaceful."
Iranian state media said missiles had struck Qeshm Island on the Strait of Hormuz.
The Iranian army said it had attacked U.S. military equipment depots at Al-Adiri, latterly named Camp Buehring, in northern Kuwait, and the positions of U.S. troops at Camp Arifjan and at Camp Doha, near Kuwait City.
Iran's Revolutionary Guards said they had significantly damaged a surveillance tower used by the U.S. Fifth Fleet in Bahrain.
U.S. airstrikes hit Piranshahr, in West Azerbaijan Province near Iran's border with Iraq, at 9 a.m. (0530 GMT) on Friday, damaging several vehicles, according to the province’s emergency services, quoted by Iranian media.
U.S. missiles struck a Revolutionary Guards Navy headquarters in the Ziba Kenar area of the Caspian Sea province of Gilan, according to a security official in Gilan quoted by Iranian media. Gilan provincial authorities said U.S. projectiles had also struck the port city of Bandar Anzali, according to the ILNA news agency.
Four people were killed and five injured in a U.S. missile attack on the Iranian city of Ahvaz, state broadcaster IRIB said.
In a statement carried by Iran's Fars news agency, the Revolutionary Guards warned the public in the Gulf countries of potential strikes against U.S. military personnel who may be using "buildings in cities as locations to direct their crimes".
It told people to "immediately move away from areas within a 500-metre radius of covert and hidden locations used by U.S. military personnel".