President Donald Trump is labeling as a "lie" a report by Iran that it has arrested 17 Iranian nationals recruited by the Central Intelligence Agency to spy on the country's nuclear and military sites.

Speaking to reporters at the White House on Monday, Trump said, "That's totally a false story. That's another lie."

An Iranian intelligence official told a news conference in Tehran that the arrests took place over the past months, and that those taken into custody worked on "sensitive sites" in the country's military and nuclear facilities.

The announcement comes as Iran's nuclear deal with world powers is unraveling and tensions spike in the Persian Gulf region.

The official did not give his name but was identified as the director of the counterespionage department of Iran's Intelligence Ministry. Such a procedure is highly unusual in Iran; officials usually identify themselves at press conferences.

The official said some of those arrested worked in nuclear and military sites. He claimed none had succeeded in their sabotage missions.

Trump also said Iran has "disrespected" the United States, and that it is "getting harder" for him to make a deal with Iran.