The local governor's office initially reported seven killed after the 6.5-magnitude quake struck late Monday, but gradually reduced that figure to four, the Mehr news agency reported.
Scientists were quoted as saying that the quake could have caused a "national catastrophe" if it had hit more densely populated areas.
According to Kerman governor Ismael Najar, the casualties were mainly in the villages of Chah Qanbar, Tak Seyfeldini and Sarze Rigan where the population is rather low.
State television said that due to the timely dispatch of relief and Red Crescent teams to the quake-hit sites, many people could be rescued from the debris overnight.
Kerman province was hit in December 2003 by a devastating earthquake which killed more than 30,000 people in the city of Bam and nearby villages.
Published 21 December 2010, 12:21 IST