The first quake of magnitude 5.9 struck on Tuesday morning 56 km north of Kerman, a city with a population of more than 820,000.
The tremor, initially reported as a magnitude 6.2 before it was revised downward, was followed by dozens of smaller aftershocks.
During the night, early on Wednesday, a stronger quake of magnitude 6.0 struck the same area. It was shallower - only 10 km deep, which would have amplified the shaking.
The latest quake was centered 64 km north of Kerman, and struck just after 1 a.m., the USGS said.
It was not immediately known if the second quake had caused any damage, injuries or fatalities as it struck during the night.
Pictures posted on state media showed groups of people standing in streets in the quake zone, fearing the collapse of buildings. The 20 damaged buildings were mostly older structures, state media reported. The pictures showed collapsed mud brick walls.
On Monday, another quake, which Iranian state media reported at 6.0 and the USGS reported at 5.4, hit western Iran, in the same region where a magnitude 7.3 earthquake killed at least 530 people last month. There have been no reports of deaths or injuries from Monday's quake.
Hardline rivals of President Hassan Rouhani have criticised the government's response to last month's quake as too slow and inadequate.