The aircraft carrier USS Harry S. Truman (CVN 75) transits the Straight of Hormuz.
The dispute comes after Iran and six world powers, including the US, reached a historic deal in July that will remove certain US, EU, and UN sanctions on Tehran in exchange for Iran accepting curbs on its nuclear program.
On Wednesday, the Obama administration began preparing new sanctions that would target nearly a dozen companies and individuals in Iran, the United Arab Emirates, and Hong Kong for their suspected role in helping develop Iran's missile program and supporting human-rights abuses and
"The naval forces of the Guards have not had any exercises in the Strait of Hormuz during the past week and the period claimed by the Americans for them to have launched missiles and rockets," the Revolutionary Guards website quoted Ramezan Sharif, the Guard's spokesman, as saying.
"The publication of such false news under the present circumstances is akin to psychological warfare," Sharif said.
NBC News, citing unnamed US military officials, said the Guards were conducting a live-fire exercise and the US aircraft-carrier Harry S. Truman came within about 1,500 yards (meters) of a rocket as it entered the Gulf with other warships.
Google Maps/Amanda Macias/Business Insider
A map of the area where the incident is said to have taken place
Cmdr. Kyle Raines, the US Central Command spokesman, described the incident as "uncharacteristic of most interactions" between the US and Iranian navies, CNN reports.
"While most interactions between Iranian forces and the US Navy are professional, safe, and routine, this event was not and runs contrary to efforts to ensure freedom of navigation and maritime safety in the global commons," Raines said.
According to the Pentagon, the USS Harry S. Truman was operating in an "internationally recognized maritime traffic lane" when Iran's navy conducted their exercise.
Iranian and US forces have clashed in the Gulf in the past, especially during the Iran-Iraq war in the 1980s after the 1979 Islamic revolution.
Diplomats have held out hope that the deal over Iran's disputed nuclear program could ease decades of mistrust and reduce tensions in the Middle East.
The West has long suspected the program was aimed at creating a nuclear bomb, something denied by Iran, which sent a shipment of low-enriched uranium materials to Russia this month as part of the deal.