(AFP) - A ceasefire between Iran and the United States was teetering Monday as the two countries traded fire over the strategic Strait of Hormuz and the United Arab Emirates reported attacks for the first time since the truce was declared nearly a month ago.

A day after President Donald Trump announced an operation to escort trapped vessels through the strait, Fox News quoted him as threatening that Iran would be "blown off the face of the earth" if it attacks US ships.

Iran appeared undaunted as it vowed to keep exerting control over the Strait of Hormuz, the narrow waterway through which one-fifth of the world`s oil flowed before the United States and Israel attacked Iran on February 28.

A US admiral said US forces sank six small Iranian ships. The Islamic republic on Tuesday denied any combat vessels had been hit, but accused the US of killing civilians on boats.

US forces "attacked two small boats carrying people... they martyred five civilian passengers and must be held accountable for their crime," Iranian state TV posted on Telegram.

The UAE, a close US ally and key Arab partner of Israel, said it came under a barrage of missiles and drones from Iran.

"These attacks represent a dangerous escalation and an unacceptable transgression, posing a direct threat to the state`s security, stability, and the safety of its territories," the UAE`s foreign ministry said in a statement.

A strike targeting an energy installation in the emirate of Fujairah injured three Indian nationals, UAE authorities said.

Two people were also injured when a residential building was hit in Oman`s Bukha along the coastline of the Strait of Hormuz, state media reported.

- Return to war footing -

Oil prices climbed further after the UAE attack, with the benchmark international contract Brent crude for July delivery jumping more than five percent.

The soaring energy costs for consumers since the war have caused economic pain around the world and created a political headache for Trump months before congressional elections.

In Israel, a military official said forces were on high alert.

The UAE ordered all schools to return to remote learning for the rest of the week.

According to the UAE defence ministry, four cruise missiles were launched from Iran, with three successfully shot down and another falling into the water.

Iran also fired drones at a tanker affiliated with its state-owned oil giant ADNOC, UAE authorities said.

A senior Iranian military official did not deny the strikes but said that the Islamic republic had "no pre-planned programme to attack the oil facilities in question".

"What happened was the product of the US military`s adventurism to create a passage for ships to illegally pass through" the Strait of Hormuz, the official said, according to state television.

"The US military must be held accountable for it," the official added.

But Iranian Foreign Minister Abbas Araghchi -- seen as a moderate in the cleric-run state in which top leaders have been killed by Israel -- said that the clashes in the strait showed there was "no military solution to a political crisis" and pointed to Pakistan`s efforts to keep mediating.

"The US should be wary of being dragged back into quagmire by ill-wishers. So should the UAE. Project Freedom is Project Deadlock," he wrote on X.

- US flexes muscle in strait -

Trump has repeatedly demanded that Iran reopen the Strait of Hormuz -- which was open before the war and which Tehran considers a main point of leverage.

On Sunday, Trump announced what he called "Project Freedom" to guide ships from neutral countries out of the Gulf, saying it was a humanitarian effort to help their stranded crews.

Much remained unclear about how the plan would operate and how the United States would assist.

US Central Command said Monday that guided-missile destroyers had transited Hormuz and that, as a first step in "Project Freedom", two US-flagged merchant vessels had travelled out of the Gulf.

But Iran`s Revolutionary Guards denied the US statement, saying: "No commercial vessels or oil tankers have passed through the Strait of Hormuz in the past few hours."

Seoul said on Monday that an "explosion and fire" had struck a South Korean ship in the strait.