It happened in the Strait of Hormuz after the Iranians failed to respond to requests by the USS Mahan to slow down, but made radio contact to question the ship’s crew about course and speed.
A helicopter dropped a smoke float and the destroyer launched flares but the boats continued at speed, according to the officials speaking anonymously to Reuters.
The Islamic Revolutionary Guard vessels are said to have come to within 800m of the Mahan, which was escorting two other US ships.
The Strait of Hormuz is a narrow passage that leads from the Persian Gulf to the Arabian Sea.
A large portion of the world’s oil passes through the strait on tankers, making it a strategically important route.
There have been similar incidents between the US Navy and Iranian boats in the area, with Iran threatening to close off the route in 2011.
President-elect Donald Trump said in September that any Iranian vessels that harass American ships in the Gulf would be “shot out of the water”.