The radio station, which is usually reliable, said the two approached the police patrol as if to seek information before setting off an explosive device.
Authorities did not immediately confirm an attack, and phones at the embassy went unanswered.
Police taped off the area around the blast site, which was littered with debris. The flag of the United States could be seen fluttering in the background.
Dozens of people have been killed in multiple attacks by Islamic extremists in Tunisia, notably in 2015 when the famed Bardo Museum outside the capital and a luxury beach hotel were attacked.
The U.S. Embassy, located in a residential area on the outskirts of Tunis, was attacked in 2012 by crowds angered by an anti-Muslim film produced in the United States. Since the fall of Tunisia’s hard-line secular dictatorship in January 2011, Salafists have come into the open.