Cabinet ministers said the renewed rocket assaults in the Israeli desert region should prompt comprehensive military action by Israel against militants behind the attacks.
The rockets targeted the cities of Ashkelon and Sderot, resulting in some vehicle and property damage beyond the civilian injuries.
Haaretz said eight rockets were fired at Sderot and another five hit Ashkelon.
The Israeli military responded to the attacks by having an air force jet fire a missile at a suspected rocket launch site. That attack resulted in two suspected gunmen being injured, Haaretz said.
The Jerusalem Post said Industry, Trade and Labor Minister Eli Yishai is among ministers calling for a response to the attacks.
"In practice, there is no truce, and we cannot tolerate a situation in which Sderot and Gaza belt residents are abandoned," Yishai said. "There is a deterioration that must be dealt with."