The strikes come hours after President Donald Trump rejected a report he was close to a compromise deal with Tehran.
The escalation in hostilities highlighted threats to the tenuous ceasefire between the US and Iran that took effect in early April, dampening hopes for a peace deal and sending oil prices surging again.
The US official, who requested anonymity to speak candidly about military operations, told Reuters the military shot down four Iranian attack drones and struck a ground control station in the port city of Bandar Abbas that was about to launch a fifth drone.
"These actions were measured, purely defensive and intended to maintain the ceasefire," the official said.
The Islamic Revolutionary Guard Corps said it targeted a US base in response to what it described as an early morning US attack near Bandar Abbas airport, Tasnim news agency reported.
The IRGC said it targeted the US airbase from which the attack on the control station near Bandar Abbas was launched, without identifying the base. Kuwait - which hosts a large US base - said it was responding to missile and drone attacks without saying where the attacks were coming from.
Israel, which has been fighting Iran-backed Hezbollah militants in southern Lebanon, also reported sounding sirens regarding hostile aircraft activity in northern Israel.
Oil prices, having fallen 5 per cent on Wednesday, rebounded after reports of the escalation in hostilities. US crude futures gained more than 3 per cent, while stocks fell and the dollar rose.
The war has killed thousands and sent global energy prices sharply higher since it began on February 28 with US and Israeli strikes.
Trump has repeatedly said the end of the war is close but told media at a cabinet meeting on Wednesday he was not yet satisfied on a deal with Iran and the US was not discussing easing sanctions on it.
He dismissed an Iranian state TV report that it had obtained an unofficial draft of an agreement to restore commercial shipping through the strait to prewar levels within a month, with Iran and Oman jointly managing traffic.
Trump said no single country would have control over the waterway, and appeared to threaten Oman, a country with which the US has decades-long military and economic ties.
"Nobody's going to control (the strait)," Trump said. "It's international waters and Oman will behave just like everybody else or we'll have to blow them up. They understand that, they'll be fine."
Iran was insisting on the United States releasing Iranian funds, the deputy secretary of its National Security Council said, according to a Tasnim report.
"We are seeking the release of all Iranian assets blocked by the United States, and this is the legal right of the Iranian nation," Ali Bagheri Kani said. "Iran's assets must be fully and unconditionally returned to Iran."
Ongoing sanctions, the dismantling of Iran's nuclear capacity and the blockage of the Strait of Hormuz, which handled a fifth of the world's oil and liquefied natural gas traffic before the war, are the major sticking points in talks to end the three-month conflict.
The waterway is covered by international law that guarantees foreign vessels the right to pass through.
The US Treasury Department added the Persian Gulf Strait Authority, the Iranian body set up to manage passage through the strait, to a list of sanctioned people and entities seen as posing threats to US national security.
With AP
