One Qassam rocket shocked several people when it struck the top of a mini-market in Sderot, Ynetnews.com reported Sunday.
Three other rockets also reportedly detonated in Sderot, hitting an industrial area, a graveyard and residence. The Eshkol Regional Council also was blasted later in the afternoon, the report said.
Authorities did not report any injuries from the rocket fire.
The attacks came after Palestinians in Gaza said Israeli soldiers killed a 41-year-old Palestinian man near his home in Khan Younis.
The Israeli military verified the operation, saying Givati and armored corps soldiers shot at an armed man.