Incoming rocket sirens continued to wail throughout southern Israel, including the city of Ashkelon, as projectiles continued to be launched from the Gaza Strip on Thursday as Israeli jets and tanks continued to pound the coastal enclave.
Three Israelis were also injured from the strikes, none of which are believed to be serious.
A Hamas militant was killed in one strike, with at least 12 others injured, the health ministry in Gaza said.
Israel's Foreign Ministry on Thursday issued an official condemnation of the BBC for its skewed reporting on Israel and the rocket attacks it has endured from Hamas in Gaza, demanding that it change its biased headline.
Only in the early afternoon did the first signs of calm appear, with Hamas saying it will halt rocket fire.
A senior Israeli military official said Thursday that the army is "nearing war with Gaza" and would evacuate Israelis living in communities adjacent to the border if necessary.
The latest flare-up in the south came as negotiations over a long-term ceasefire - mediated by the United Nations and Egypt - continued.
Israel Hayom's Yoav Limor says Hamas doesn't want war and Israel doesn't know what it wants: Ministers who met this week are mostly leaning toward a calm, despite the fact that the way there is long and complicated, and doesn't offer much more than quiet.
It was the third severe flare-up of violence since July and came despite attempts by United Nations officials and Egypt to secure a long-term truce between Israel and Hamas.
In Gaza, one Hamas militant was killed in the air strikes, as was a Palestinian woman and her 18 month old child, Palestinian officials said.
The incident occurred while a group of senior Hamas leaders from overseas were visiting Gaza to discuss the ceasefire efforts with local leaders.
Hamas military wing, Ezzeddin al-Qassam Brigades, identified the victims of Tuesday's Israeli strike as Ahmed Murjan and Abdel-Hafez al-Silawi.
Thirty of rockets were intercepted by the Iron Dome missile defense system, which is activated only against those projected to hit populated areas, whilst the majority of the projectiles fell in open areas.
Nickolay Mladenov, the UN's special coordinator for the Middle East peace process, said on Wednesday he was "deeply alarmed by the recent escalation of violence between Gaza and Israel, and particularly by today's mutiple rockets fired towards communities in southern Israel".
The Palestinian government has issued a statement calling for immediate worldwide intervention to stop Israel's aggression against the blockaded enclave. "If the current escalation however is not contained immediately, the situation can rapidly deteriorate with devastating consequences for all people".
Clashes along the Gaza border since the end of March have seen at least 165 Palestinians killed by Israeli fire.
One Israeli soldier has been shot dead by a Palestinian sniper. But it has come under heavy global criticism for its frequent use of force against unarmed protesters.
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