A Grad rocket directly struck a home in the southern city of Be'er Sheva on Saturday night, killing one person and seriously wounding four.
26 people are being treated for shock.
Another Grad rocket fired at Be'er Sheva was intercepted by the Iron Dome system.
Also on Saturday evening, two children were lightly wounded when four Grad rockets landed in Ofakim.
The Popular Resistance Committees claimed responsibility for the Be'er Sheva rocket attacks while Hamas claimed responsibility for the Ofakim rocket attacks.
Israel's "Forum of Eight" senior government ministers is expected to meet late Saturday night to weigh possible responses to the rocket attacks.
Rocket and mortar attacks took place throughout southern Israel on Saturday.
Overall, around 50 Qassam rockets, Grad missiles and mortar shells have been fired at southern Israel from the Gaza Strip since Thursday evening, wounding 16 people.
Early on Saturday, one person was lightly wounded by a rocket that landed in an open area near Be'er Sheva, while seven others received medical attention either for sustaining wounds while seeking shelter, or for shock.
Throughout the day, a number of rockets and mortar shells landed in the Eshkol and Sha'ar Hanegev regions.
Two rockets also fell in the Be'er Tuvia Regional Council, and another near the city of Ashkelon. No injuries or damage were reported.
On Saturday morning, several Grad rockets fired from the Gaza Strip hit the southern city of Ashdod, wounding three people.
Magen David Adom treated three young men for shrapnel wounds in their chests and necks.
Due to rocket fire, the IDF Homefront Command and local municipal authorities have cancelled public events, including concerts and soccer matches, throughout the south.
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