By Jana Choukeir, Enas Alashray and Phil Stewart

DUBAI/WASHINGTON, May 28 (Reuters) - Iran's Revolutionary Guard said on Thursday it targeted a U.S. airbase after the U.S. military carried out what a Washington official said were strikes targeting an Iranian drone operation near the Strait of Hormuz, 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 U.S. and Iran that took effect in early April, dampening hopes for a peace deal and sending oil prices surging again.

The U.S. 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 U.S. base in response to what it described as an early morning U.S. attack near Bandar Abbas airport, Tasnim news agency reported. The IRGC said they targeted the U.S. airbase from which the attack on the control station near Bandar Abbas was launched.

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.

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 more than 5% on Wednesday, rebounded after reports of the escalation in hostilities. U.S. crude futures gained more than 3%, 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 since it began on February 28 with U.S. and Israeli strikes. Trump has repeatedly said that a deal is close at hand.

At a cabinet meeting attended by media on Wednesday, Trump 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 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."

Trump added that he was not yet satisfied on a deal with Iran and the U.S. was not discussing easing sanctions on the country.

The White House and Oman's embassy in Washington did not immediately respond to a request for comment.

Iran's permanent mission to the United Nations was not immediately available for comment.

The Iranian TV report of a framework deal said the United States would also lift its blockade of Iranian ports and withdraw military forces from Iran's vicinity.

Ebrahim Azizi, head of the Iranian parliament's national security committee, said Trump’s “rhetoric” would not force Iran to back away from its demands to enrich uranium, wield authority over the strait and see sanctions against it lifted.

"It is obvious Trump, seeking a way out of this strategic deadlock, alternates between issuing threats and appealing for an agreement," Azizi said in a post on X.

The strait, which handled a fifth of the world's oil and liquefied natural gas traffic before the war, the dismantling of Iran's nuclear capacity and ongoing sanctions are the sticking points in talks seeking to end the three-month 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.

The Iranian TV report on the draft agreement did not mention Iran's nuclear program, which the U.S. wants disbanded.

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.

(Reporting by Reuters' bureaux; Writing by Lincoln Feast; Editing by Stephen Coates)

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