In a written statement carried by the official social media accounts of Iran's supreme leader and Iranian state media, Supreme Leader Ayatollah Mojtaba Khamenei said U.S. actions have shown that Trump's signature was "utterly worthless and devoid of credibility."
The statement warned of "even heavier costs and further humiliation" for the United States. The White House did not immediately respond to a request for comment.
Khamenei's whereabouts remain a mystery.
The conflict, which began when the U.S. and Israel launched strikes on Iran at the end of February hoping to disable its nuclear and missile programmes and degrade its regional proxies, has led to major disruption to energy supplies, fears over global inflation and a battle for control of the Strait of Hormuz.
On Saturday, Kuwait came under sustained attack, with the armed forces saying they had intercepted Iranian ballistic missiles and drones, and that some firefighters and oil sector workers had been injured while responding to the attacks.
Iran's IRGC said it had struck a U.S. military support centre at Kuwait's Camp Arifjan and destroyed a radar facility at Ali Al Salem Air Base, Iranian media said. Kuwait Petroleum Corporation later said one of its oil facilities had been hit in "repeated Iranian attacks", causing significant damage and some injuries, according to the state news agency.
The IRGC also targeted a site in Bahrain where U.S. combat aircraft were gathered at Sheikh Isa Air Base and an intelligence data centre, Iranian media said.
The Guards also destroyed at least two U.S. fighter aircraft and three other aircraft during a missile and drone attack early on Saturday on the U.S. base in Al Azraq, Jordan, according to Iranian state TV.
Reuters could not independently verify the reports.
Saudi Arabia's early warning system issued alerts early on Saturday urging residents of Al-Kharj and Yanbu to seek shelter. Al-Kharj, east of Riyadh, is home to a military base that hosts U.S. troops, while Yanbu, on the Red Sea, has a key oil export terminal.
Two people briefed on the matter said an Iranian missile attack, the first on Saudi Arabia in more than three months, had triggered the alerts. The government media office did not respond to a request for comment.
The IRGC made no mention of any attack on Saudi Arabia.
The U.S. State Department issued a worldwide travel alert for Americans abroad on Saturday, citing heightened tensions in the Middle East "with the potential for unforeseen escalation." The advisory said flight cancellations and periodic airspace closures could disrupt travel.
Earlier, U.S. Central Command said it had hit Iranian surveillance sites, military logistics infrastructure, underground weapons storage and maritime capabilities.
U.S. airstrikes early on Saturday killed three people and wounded eight others in the southern Hormozgan province, which borders the Strait of Hormuz, while two bridges and a road tunnel were damaged, Iranian state TV reported.
Iran's Health Ministry said on Saturday that 50 people had been killed and more than 500 wounded in U.S. strikes on the country over the past three weeks.
Iranian Foreign Ministry spokesperson Esmaeil Baghaei accused the United States of seeking control over the Strait of Hormuz, which usually handles around one-fifth of the world's oil supply.
Both sides have taken aim at shipping traffic, with the U.S. saying it is enforcing a naval blockade and Iran saying it targets vessels violating its rules on navigating the strait.
The European Union and Gulf states called on Iran to immediately and unconditionally halt all attacks and interference with maritime navigation and to keep the strait open without conditions or fees, according to a joint statement reported by Saudi state TV on Saturday.