Donald Trump has said Iran is lying about having arrested 17 Iranian nationals recruited by the CIA to spy on the country’s nuclear and military sites.

“That’s totally a false story. That’s another lie,” the US president told reporters at the White House.

In Tehran, an intelligence official told a news conference that the arrests took place over recent months, and those taken into custody worked on “sensitive sites” in military and nuclear facilities.

Intelligence chiefs said some of the 17 have already been sentenced to death, but did not say how many.

Mr Trump also said Iran has “disrespected” the US, and that it is “getting harder” for him to want to make a deal with Tehran to replace the 2015 nuclear deal he pulled out of last year.

He called Iran a “very mixed up country” with big economic problems and a restive population.

“They have a lot of problems,” he said. “So, whatever it is, I’m just going to sit back and wait” to see whether Tehran will agree to negotiate limits on its nuclear programme and other activities.

“If they want to make a deal, frankly it’s getting harder for me to want to make a deal with Iran because they’ve behaved very badly. They’re saying bad things.”

The Iranian official said the 17 were recruited by the CIA and had “sophisticated training” but did not succeed in their sabotage missions. Their spying missions included collecting information at the facilities where they worked and installing monitoring devices, he said.

He added that some were staff members at the targeted facilities, and the rest were working as consultant and contractors. The official said the CIA had promised them US visas or jobs in America.

Tensions with the West escalated on Friday when Iran seized a British-flagged oil tanker in the Strait of Hormuz. On Monday, British Foreign Secretary Jeremy Hunt accused Tehran of “an act of state piracy” that he said must be met with a co-ordinated international reaction.

In his comments in the Oval Office, Mr Trump also claimed “there’s a lot of proof” that the US destroyed an Iranian drone last week over the Strait of Hormuz, although the US has provided no public evidence. Iran denies it lost a drone.

The president appeared to confirm news reports that the USS Boxer used an electronic jamming device to bring down the drone, rather than shoot it down with a missile or other conventional weapon.

“The drone came down, you know how it came down, with a new technology that’s actually quite amazing,” he said.

The US military last week refused to say what kind of weapon it used against the drone.