There were no immediate reports of damage or casualties following the earthquake, which happened at 8:41 pm (1711 GMT), the agency said.
The first tremor, at 1:53 pm (1023 GMT), killed nine people and injured around 70 on the Gulf island, home to some 100,000 people and situated off the coast from the large port city of Bandar Abbas.
Iranian state television put the intensity of that quake at 5.9 on the Richter scale.
The US Geological Survey put the magnitude slightly higher at 6.1 while a seismic observatory in the French city of Strasbourg put it at 5.6.