Iran targeted a U.S. air base on Thursday after the United States struck what Washington described as an Iranian drone operation near the Strait of Hormuz and President Donald Trump rejected a reported compromise deal with Tehran.

The attacks, while limited, highlighted the fragility of negotiations aimed at turning the tenuous ceasefire that took effect in early April into an agreement to end the three-month-old war and reopen the vital shipping route.

A U.S. official 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," said the official, who requested anonymity to speak candidly about military operations.

The Islamic Revolutionary Guard Corps said later that it had targeted the U.S. base responsible for an early-morning attack near Bandar Abbas airport, Tasnim news agency reported.

The IRGC, which did not name the base, said any repeat of what it called aggression would lead to a "more decisive" response.

Kuwait - which hosts a large U.S. base - said it was responding to missile and drone attacks without saying where the attacks were coming from.

In Lebanon, which Iran says must be part of any overall agreement to end the war launched by Israel and the United States on February 28, Israel said it had begun striking infrastructure of Iran-backed Hezbollah militants in Tyre.

The Lebanese army said an Israeli strike had killed one of its soldiers, while Israel, which has pushed deep into Lebanon in pursuit of Hezbollah, said hostile aircraft infiltration had triggered sirens in its north.

Oil prices rebounded, with U.S. crude futures CLc1 up around 2.5% after falling 5% on Wednesday, while stocks fell and the dollar rose.

TRUMP SAYS NO COUNTRY TO CONTROL STRAIT

The war has killed thousands and sent global energy prices sharply higher, fuelling inflation and hitting currencies in some Asian countries while boosting the dollar.

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 by the talks with Iran and that the U.S. was not discussing easing sanctions on the country, one of Tehran's demands.

He dismissed an Iranian state TV report about an unofficial draft of an agreement to restore commercial shipping through the strait to prewar levels within a month, with Iran and Gulf state 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 U.S. 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."

Oman has not said anything about the idea of joint control of the strait with Iran, with which it says it has discussed freedom of navigation. Iranian Foreign Ministry spokesperson Esmaeil Baghaei expressed solidarity with Oman after what it called "U.S. officials' threats".

Iran was insisting on the United States releasing Iranian funds, the deputy secretary of its National Security Council Ali Bagheri Kani said, according to a Tasnim report.

Ongoing sanctions, the dismantling of Iran's nuclear capacity and the blockage 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 conflict.

The waterway is covered by international law that guarantees foreign vessels the right to pass through.

The U.S. 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 U.S. national security.

Iranian state TV said the draft deal would also have the U.S. withdraw military forces from the immediate vicinity, though it said the issue of U.S. troops in the region needed further discussion. The White House dismissed the report as a "complete fabrication." Tehran did not comment.

Iran's nuclear program, which the U.S. wants disbanded, was not mentioned in the Iranian TV report.

Iranian sources have said talks on the nuclear issue will come in a second round of negotiations - something that may not be acceptable to some of Trump's closest supporters. Iran says its nuclear program is for peaceful purposes only.

"The bottom line is Iran's never going to have a nuclear weapon," U.S. Secretary of State Marco Rubio said at the cabinet meeting.